Question

This figure shows two shaded regions and a non-shaded region. Angles in the figure that appear to be right angles are right angles.

Part A:
What is the area, In square inches, of the triangular-shaped region that is shaded in this figure?
Part B:
What is the area, in square inches, of the non-shaded region in this figure?

Answer 1

Part A: 4 in.²

Part B: 35 in.²

Explanation:

Part A:

The base of the triangle is 2 inches.

The height of the triangle is 4 inches.

A = bh/2

A = (2 in.)(4 in.)/2

A = 4 in.²

Answer: 4 in.²

Part B:

The non-shaded region of the figure can be broken down into several simple shapes:

Top right - a square 2 inches by 2 inches.

Below the square - a triangle congruent to the shaded triangle.

Bottom left - a rectangle 6 inches wide and 4 inches tall

Above the large rectangle - a smaller rectangle 3 inches by 1 inch.

The total non-shaded area is the sum of the areas of the simple shapes above.

All linear dimensions are inches, and the area is in square inches.

A = 2 × 2 + 4 + 6 × 4 + 3 × 1

A = 4 + 4 + 24 + 3

A = 35

Answer: 35 in.²