The diagram shows a square ABCD
M is the midpoint of AB
N is the midpoint of AD
The area of the shaded triangle AMN is 8cm^2
Work out the area of triangle MCN

The Diagram Shows A Square ABCDM Is The Midpoint Of ABN Is The Midpoint Of ADThe Area Of The Shaded Triangle

Answers

Answer 1
Maybe şt can be happen but ım not sure 26
Answer 2

The area of the triangle, Δ AMN is 8 cm², so the area of the triangle, ΔMCN is 24 cm².

A triangle is one of the most basic geometric figures with 3 sides, 3 angles, and 3 vertices.

The area of a triangle is half of the product of the base and height.

Given that

ABCD is square and M and N are mid-points of lines AB and AD respectively.

Area of triangle, ΔAMN = 8 cm²

[tex]\dfrac{1}{2} \times AN \times AM = 8\\AN \times AM = 8 \times 2\\AN \times AM = 16[/tex] ...(i)

Since ABCD is square, therefore AB = AD.

Also, as M and N are mid-points of lines AB and AD, so

AN = AM.

Substitute AN = AM in equation (i),

[tex]AN \times AN = 16\\AN^2 = 16\\AN = \sqrt{16}\\AN = 4\ cm[/tex]

So,

AD = 2 × AN

     = 2 × 4

     = 8 cm

As ABCD is square,

AB = BC = CD = AD = 8 cm.

Area of the square ABCD = 8² = 64.

Since CD = BC, ND = MB, ∠D = ∠B.

Therefore by SAS property of similarity,

ΔCDN ≅ ΔCBM

Area of the triangle, ΔCDN = Area of the triangle, ΔCBM.

                                              [tex]= \dfrac{1}{2} \times CB \times BM\\= \dfrac{1}{2} \times 8 \times 4\\\\= 16\ cm^2[/tex]

Area of the triangle, ΔCMN = Area of ABCD - Area of ΔAMN - Area of ΔCDN - Area of ΔCBM

Area of the triangle, ΔCMN = 64 - 8 - 16 - 16

                                              = 24 cm²

Therefore, the area of ΔCMN  is 24 cm².

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Related Questions

Please answer! I will mark you Brsinliest! The pictures are together.

Answers

Answer:

V = 65.97π

Step-by-step explanation:

Answer:

g00gle is a really great source for these questions!

Just put in the information and they do they work!

Step-by-step explanation:

66 inches cubed since you round up .03 decimals!

or 65.97 if you aren't supposed to round

Parallelogram PQRS has diagonals that are perpendicular. Based on that, which statement is most correct?

A- Parallelogram PQRS is also a rectangle

B- Parallelogram PQRS is also a rhombus.

C- Parallelogram PQRS is neither a rectangle nor a rhombus.

D- Parallelogram PQRS is both a rectangle and a rhombus, so it is a square.

Answers

Answer:

B- Parallelogram PQRS is also a rhombus.

Step-by-step explanation:

Given

Parallelogram PQRS with perpendicular diagonals

Required

Which of the option is true

(a) PQRS can be a rectangle

A rectangle do not have perpendicular diagonals.

Hence, (a) is false

If (a) is false, then (d) is also false

(b) PQRS can a rhombus

The diagonals of a rhombus are not perpendicular.

So (b) is true

No need to check for (c), since only option is true

Answer:

B- Parallelogram PQRS is also a rhombus.

Step-by-step explanation:

Hope this helps

What is the MEAN of the data - (12, 8, 6, 12, 16, 12) *

helppp

Answers

Answer: the mean is 11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Add them all together then divide by the nuber of variables

At the tasty bakery, cupcakes cost fifty cents each.Doughnuts cost a dollar twenty five.How much more do two doughnuts cost than two cupcakes?

Answers

Answer:

$1.50

Step-by-step explanation:

The computation is shown below:

Given that

The cost of each cupcakes be 0.50 cents

And, the cost of doughnuts be $25

So for two doughnuts the cost would be 2.50

And, for two cupcakes, the cost would be 0.50 × 2 = 1

So, the more amount would be

= 2.50 - 1

= $1.50

Hence, the same would be considered and relevant too

anyone know ??? i need help badly right now

Answers

Answer:

Answer is A 520mm²

I hope you like it

Answer:

9. C, II and III.

10. The correct answer is 944 cubic mm, as far as I can tell. I double checked my formulas and calculations. You can copy the formulas/calculations below and email your teacher. I have tried to figure out how they got the numbers they have. The best guess I can come up with is that they used 6 as the diameter of the cylinder, using 3 for the radius. That gets us closer, at 749 cubic mm, but not quite there.

Step-by-step explanation:

9.  If the cylinder is standing upright, the horizontal cut would be a circle or oval, and the vertical cut could be a rectangle

10. First we'll get the volume of the base rectangle. Then we'll calculate the volume of a cylinder, then divide that part in half, because it's 1/2 a cylinder on top of a rectangular prism.

Volume of a rectangular prism:

V = (length)(width)(height)

= 11 x 9 x 6 = 594 cubic mm

Volume of a cylinder:

V = (pi)(radius)^2(height)

The radius = 1/2 the diameter of the circle...the diameter is 9, so the radius is 4.5

= (3.14)(4.5)(4.5)(11)

= 699.435

That would be for a full cylinder with radius 4.5 and height of 11. We have half of one, so 699.435/2 = 349.7175 cubic mm

Add the volume of the 1/2 cylinder to the volume of the rectangular prism:

349.7175 + 594 = 943.7175, rounded = 944...which is none of your answers :/

Sorry I couldn't give you an "A, B, C, D" answer, but I don't think any of those are correct.

The equation of the scatter plot trend line is y = -1700x + 32000 where y is the value of the car in dollars and x is the age of cars in years. Use the trend line equation to predict the value of a car after 7 years.

Answers

Answer:

20100

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Given equation

y = -1700x + 32000

Where x is the age of car and y is the value of the car.

Then value after 7 years can be calculated as follows,

y = -1700 (7) + 32000

y = -11900 + 32000

y = 20,100

So, the value of car after 7 years will be 20100.

what is the sale price of $149 sneakers with 15% off?

Answers

Answer:  $ 126.65

Step-by-step explanation:

149/100)*15 =

(149*15)/100 =

2235/100 = 22.35

15% of $149 is 22.35

so ,

   real price-15% of real price= sale preice

  $149-$22.35=$126.65

Answer:

$ 126.65

Step-by-step explanation:

$ 149 multiply 15 % which is 0.15

Which is $ 22.35

Take $ 149 - $22.35 = $126.65

A psychologist takes an SRS of 404040 people in their twenties and 606060 people in their fifties and surveys them about their anxieties. Suppose that 48\%48%48, percent of people in their twenties and 28\%28%28, percent of people in their fifties have anxiety about flying. The psychologist will then look at the difference (\text{20's}-\text{50's})(20’s−50’s)left parenthesis, start text, 20, apostrophe, s, end text, minus, start text, 50, apostrophe, s, end text, right parenthesis between the proportions of people with anxiety about flying in each sample. What will be the shape of the sampling distribution of the difference in sample proportions, and why?

Answers

Answer: Approximately normal, because we expect 19.2 successes and 20.8 failures from people in their twenties, and 16.8 and 43.2 from people in their fifties, and all of these counts are at least 10.

Step-by-step explanation:

What is the value of x?
a . 75
b . 25.5
c . 8
d . 4.5

help meeee

Answers

Answer:

d. 4.5

Step-by-step explanation:

10x-5=16x+22

    -22      -22

10x-27=16x

-10x      -10x

-27=6x

x=4.5

The answer is d 4.5

Work out size of Angle x

Answers

Answer:

106

Step-by-step explanation:

all 3 of the angles add up to 360

you already know one is 164 and one is a right angle so

164 + 90 = 254

360 - 254 = 106

Find the 11th term of the geometric sequence 6, -18, 54, ...

Answers

Answer:

354294

Step-by-step explanation:

Use the formula

[tex]a_{n} = a_{1} r^{n - 1}[/tex]

In your problem [tex]a_{1}[/tex] = 6   r = -3    n = 11

11th term = [tex]a_{11}[/tex] = [tex]6(-3)^{11 - 1} = 6(-3)^{10}[/tex] = 6(59049)

                       = 354294

What is the volume, in cubic feet, of this composite figure? (Do not write
the units.) *
1 ft
2 ft
5 ft
3 ft
9 ft

Answers

I think the answer is 5

I need the answer for this question

Answers

Yup it’s b for sure

help please? anyone?

Answers

Answer:

"so i need to find e missing side of each right triangle, side c is the hypotenuse!! a = 8.8ft, b= 9ft i have to round the answers to the nearest tenth if necessary "

Step-by-step explanation:

Sure! So remember that the Pythagorean theorem is a squared plus b squared = c squared.

= 8.8 squared + 9 squared = c squared

= 77.44 + 81 = c squared

[tex]\sqrt{158.44}[/tex] = c squared

c squared = (rounded) 12.6 ft

how to do this question plz answer ​

Answers

9.95^2 x 29.8 = 2,950.2745 and Yes the answer is sensible.

A circle has a diameter of 18. The sector has a central angle of 30 degrees. What is the area of the sector?

Answers

Answer:

21.21

Step-by-step explanation:

Area of a circle is A = π r^2

Variables:

r = 18/2 = 9

θ = 30 deg

Find the area:

A = π r^2

A = π 9^2

A = 254.47

Find the area of the sector:

θ/360 * A

= 30/360 * 254.47

= 21.21

I need help please !!!

Answers

Answer:

isosceles triangle

Step-by-step explanation:

the first one is isosceles triangle

Devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 6 cm and the height of the pyramid is 9 cm. To get the wax for the candle, Devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm. How many of the wax cubes will Devin need in order to make the candle? Show your work.

Answers

The volume of the square pyramid is 6 x 6 x 9/3 = 108 cubic cm.

Volume of the cube = 4 x 4 x 4 = 64 cubic cm

Number of cubes needed: 108/64 = 1 11/16 cubes (1.6875)

Answer:

Solution given:

square pyramid

each side of base[b]=6cm

height[h]=9cm

Volume of square pyramid[V]=[tex] \frac{1}{3 } {b}^{2} h \\ \frac{1}{3} {6}^{2} \times 9 = 108cm ^{3} [/tex]

now

length of cube [l]=4cm

volume of cube[v]=l³=4³=64cm³

now

no of wax needed=[tex] \frac{V}{v} [/tex]=[tex] \frac{108cm³}{64cm³} [/tex]=[tex] \frac{27}{16 } =1\frac{11}{16} [/tex]

is needed.

Triangle ABC has AB = 10 √3cm, AC=6cm and has area 45cm^2
(i) Find the size of angle CAB.

(ii) Find the length of BC

Answers

Answer:

I) ∠CAB measures 60°.

II) BC measures approximately 15.23 cm.

*Please read notes.

Step-by-step explanation:

We are given ΔABC, where AB measures 10√3 cm, AC measures 6 cm, and the triangle has an area of 45 square cm.

And we want to find I) the measure of ∠CAB and II) the length of BC.

I) First, we should always draw a representative triangle so we can determine the sides and angles. This is shown below.

Note that ∠CAB (or simply ∠A) is the angle between the two sides. Thus, we can find the angle by using the alternative formula for the area of a triangle:

[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]

Where a and b are two side lengths, and C is the angle between the two sides.

Substitute:

[tex]\displaystyle 45=\frac{1}{2}(10\sqrt{3})(6)\sin(A)[/tex]

Simplify:

[tex]\displaystyle 45=30\sqrt{3}\sin(A)[/tex]

So:

[tex]\displaystyle \sin(A)=\frac{45}{30\sqrt{3}}=\frac{3}{2\sqrt3}=\frac{\sqrt{3}}{2}[/tex]

Take the inverse sine of both sides. Use a calculator. Thus:

[tex]\displaystyle m\angle A=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^\circ[/tex]

II) To find BC, we will use the Law of Cosines. We do not know whether or not ΔABC is a right triangle, so we cannot use right triangle trigonometry or special right triangles.

The law of cosines is:

[tex]\displaystyle c^2=a^2+b^2-2ab\cos(C)[/tex]

Where a and b are side lengths and C is the angle between the side lengths. c is the side length opposite to the angle.

BC is opposite to A. Substitute:

[tex](BC)^2=(10\sqrt{3})^2+(6)^2-2(10\sqrt{3})(6)\cos(60^\circ)[/tex]

Simplify:

[tex]\displaystyle BC^2=336-120\sqrt{3}\left(\frac{1}{2}\right)=336-60\sqrt{3}[/tex]

Take the square root of both sides:

[tex]\displaystyle BC=\sqrt{336-60\sqrt{3}}\approx 15.23[/tex]

BC measures about 15.23 cm.

Notes:

In this case, the inverse sine of √3/2 will yield two answers: 60° and 120°. This is an example of an ambiguous case. Both of these angles will work. However, BC will be different. If ∠A is 60°, then BC is about 15.23. However, if ∠A is 120°, then BC is about 20.97. Both will result in the triangle having an area of 45 square cm, as well as AB measuring 10√3 and AC measuring 6.

SIMPLEE!!! WRITE AN EXPRESSION!

Answers

2s+2(s-7). Would be an equation. Hope this helps:)

I need help with this question​

Answers

Answer:

I thinks its F because you cant factor it

Step-by-step explanation:

Answer:

F) The expression does not have a real factor

please help me solve this​

Answers

Answer:

4x^2+36x+81

Step-by-step explanation:

FOIL

First terms

Outside terms

inside terms

last terms

A man travels 2 miles, turn left and travels 3 miles, turn left again and travel 6 miles. How far is he from the starting point?​

Answers

Answer: 5 miles

Step-by-step explanation:

this creates a polygon which can be shortened to be a triangle with side lengths 3 and 4 and the hypotenuse unknown. to find the side length you use the formula a^2 + b^2 = c^2

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

sqrt(25) = c

c = 5

what's the area of this shape

Answers

Answer:

L x W x H

Step-by-step explanation:

if my calculations are correct the length is 2 the width is 3 and the height is 3

Therefore the answer is (2 x 3) = 6 x3

So the answer is 18.

Hope it helps, if it is incorrect than i am extremely sorry, wish you the best of luck and have a great day/midday/evening. BYYEEEEEEE

What problems did Title IX address? Check all that apply.

lack of support for international students

limited opportunities for female athletes

limited resources in scientific courses of study

lack of scholarships and championships for women in sports

limited resources and facilities for women

Answers

Answer:

limited resources and facilities for women

lack of scholarships and championships for women

limited opportunities for female athletes

2,4,5

Statement two, four, and five are correct title IX law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.

What is Title IX?

Title IX is a potent instrument for fighting campus violence because it is a federal (national) legislation. To ensure that all students have equal access to education, the law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.

As per the Title IX law:

Limited opportunities for female athletes.Lack of scholarships and championships for women in sports.Limited resources and facilities for women.

Thus, statement two, four, and five are correct title IX law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.

Learn more about the Titel IX law here:

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An engine is operating at 25% of its full power. Which number line shows a point that
represents 25%?

Answers

Answer:

The first line

Step-by-step explanation:

Can anyone help me I’ll mark ya Brainly

Answers

Answer:

1/6

Step-by-step explanation:

f(x) = -x^(4)

Identify the function as a translation, compression, stretch, or reflection

Answers

Answer: don't know the answer but I hope this helps.

Step-by-step explanation:

last one pls help i dont get this slope thingy

Answers

Answer:

-3

Step-by-step explanation:

Slope going down.

From point (-2,3) to (-1,0): Down 3, Over 1 (-3/1)

What is 1?1?1?1=6 pls help my brain id hurt rn​

Answers

Answer:

(1+1+1)!*1=6

Step-by-step explanation:

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