Step-by-step Solution:
We know that:
- Perimeter of shape = 112 inches
- Perimeter of shape = 20 + 20 + (4b)
- Area of triangle = 1/2 x b x a
- Area of square = b²
Work:
- 20 + 20 + (3x) = 112
- => 3x = 112 - 40
- => 3x = 72
- => x = 24 in.
This means that the side of the square is 24. This could also mean that the value of x is the base of triangle.
- => Total length of all three missing sides of square = 3(24)
- => 72 in.
Now, let's find the area of the triangle.
- => 1/2 x 24 x 16
- => 1 x 12 x 16
- => 192 in.²
Now, let's find the area of square.
- => 24² = Area of square
- => 576 in.²
Now, let's find the area of the given figure
- => 192 + 576 = Area of given figure
- => 768 in.²
Final Answer:
The total length of three sides of the square is 72 in., so the side length of the square is 24 in. The area of the triangle is 192 in², and the area of the square is 576 in², so the total area is 768 in².
