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3 years ago

Surface area of composite figures with a square and triangle

Mathematics

1 answer:

docker41 [41]3 years ago

3 0

Answer:

The length of each side of square is 5ft.

Step-by-step explanation:

Given:

A composite figure is formed by combining a square and a triangle. Its total area is 32.5ft squared.

The area of the triangle is 7.5ft squared.

Now, to find the length of each side of square.

Now, we need to get the area of the square first:

Area of combined figure - area of triangle = area of square.

32.5 ft squared - 7.5 ft squared = 25 ft squared.

So, area of square = 25 ft squared.

Now, by putting the formula for getting the length of each side:

Let the side = a.

Area of square = 25 ft squared

Area of square = a²

Using square root both sides we get:

So, the side = 5 ft.

Therefore, the length of each side of square is 5ft.

You might be interested in

Find the measure of angle X in the triangle below.

Elan Coil [88]

Answer:

X = 89.92° or 90.08°

Step-by-step explanation:

The law of sines can be used to find the value of angle X:

sin(X)/26 = sin(67.38°)/24

sin(X) = (26/24)sin(67.38°) ≈ 0.99999901787

There are two values of X that have this sine:

X = arcsin(0.99999901787) ≈ 89.92°

X = 180° -arcsin(0.99999901787) ≈ 90.08°

There are two solutions: X = 89.92° or 90.08°.

_____

Comment on the problem

We suspect that the angle is supposed to be considered to be 90°. However, the given angle is reported to 2 decimal places, so we figure the requested angle should also be reported to 2 decimal places.

The lengths of the short side that correspond to the above angles are 10.03 and 9.97 units. If the short side were considered to be 10 units, the triangle would be a right triangle, and the larger acute angle would be ...

arcsin(24/26) ≈ 67.38014° . . . . rounds to 67.38°

This points up the difficulty of trying to use the Law of Sines on a triangle that is actually a right triangle.

3 0

2 years ago

Read 2 more answers

If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

MrMuchimi

After plotting the quadrilateral in a Cartesian plane, you can see that it is not a particular quadrilateral. Hence, you need to divide it into two triangles. Let's take ABC and ADC.

The area of a triangle with vertices known is given by the matrix
M = $\left[\begin{array}{ccc} x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right]$

Area = 1/2· | det(M) |
= 1/2· | x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃ |
= 1/2· | x₁·(y₂ - y₃) + x₂·(y₃ - y₁) + x₃·(y₁ - y₂) |

Therefore, the area of ABC will be:
A(ABC) = 1/2· | (-5)·(-5 - (-6)) + (-4)·(-6 - 7) + (-1)·(7 - (-5)) |
 = 1/2· | -5·(1) - 4·(-13) - 1·(12) |
 = 1/2 | 35 |
 = 35/2

Similarly, the area of ADC will be:
A(ABC) = 1/2· | (-5)·(5 - (-6)) + (4)·(-6 - 7) + (-1)·(7 - 5) |
 = 1/2· | -5·(11) + 4·(-13) - 1·(2) |
 = 1/2 | -109 |
 = 109/2

The total area of the quadrilateral will be the sum of the areas of the two triangles:

A(ABCD) = A(ABC) + A(ADC)
 = 35/2 + 109/2
 = 72

8 0

3 years ago

A mapping statement is a way of describing a _____ of a figure

mash [69]

The answer is D transformation.

7 0

3 years ago

Solve r + (-8) = 10 ———————-

Yuliya22 [10]

Answer:

r = 18

Step-by-step explanation: