Question

The figure shown is a rectangle. The green shape in the figure is a square. The blue and white shapes are rectangles, and the area of the blue rectangle is 24 square inches.

A. Write an expression for the area of the entire figure that includes an exponent. Then find the area.

B. Find the dimensions of the entire figure.

Answer 1

A. (2 × 6) + (3 × 8) + 6²

72 sq. inches.

B. 9 in. by 8 in.

Explanation:

The white shape has dimensions of 2 in. by 6 in. and the green shape is a square.

So, the dimension of the green shape is 6 in. by 6 in.

Therefore, the length of the blue shape is (6 + 2) = 8 in.

Now, given that the area of the blue shape is 24 sq. in.

So, the width of the blue shape is
`(24)/(8) = 3` in.

Now, if we consider the total figure, then area of the entire figure = area of the white shape + area of the green shape + area of the blue shape.

= (2 × 6) + (3 × 8) + 6² (Answer)

= 12 + 24 + 36

= 72 sq, inches. (Answer)

Now, the length of the entire figure is (6 + 3) = 9 in. and width of the entire figure is (2 + 6) = 8 in.

Therefore, the dimensions of the entire figure will be 9 in. by 8 in. (Answer)