Assuming the "square" is the shape in the figure that is in the top left, we can say that the sides of that square is 6in on every side since the definition of a square is that it has the same length for every side. This means that the left side of the square is 6in and since we already have the rest of the length for the left side of the figure we know that the length of this side for the figure is 8in (6in + 2in).
This means that an expression for the area of the entire figure (including exponents) is:
The formula for the area of a rectangle/ square is (base * height)
Area = area of square + area of bottom rectangle + area of right rectangle
Area = 6 ^2 + (6*2) + area of right rectangle
To find the area of the right rectangle we have to gather what we already know:
We know that the left side of this figure is 8in. This means that the left side of the right triangle is also 8in. We are also given that the area of this triangle is 24in^2. This means that we have the expression: 24 = 8 * x
x = 24/8 .... x = 3
We now know that the bottom side of the triangle on the right is 3in.
a. Area = 6 ^2 + (6*2) + (8 * 3)
b. area = 72in ^2
