Question

Find the area of the polygon. Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.

Answer 1

To find the area of the polygon, we can divide it into smaller shapes and then find the area of each shape.

The polygon can be divided into two triangles and a rectangle.

Triangle 1:
Base = 5 units
Height = 4 units
Area = 1/2 * base * height = 1/2 * 5 * 4 = 10 square units

Triangle 2:
Base = 3 units
Height = 4 units
Area = 1/2 * base * height = 1/2 * 3 * 4 = 6 square units

Rectangle:
Length = 3 units
Width = 5 units
Area = length * width = 3 * 5 = 15 square units

Total area of the polygon = Area of Triangle 1 + Area of Triangle 2 + Area of Rectangle
= 10 + 6 + 15
= 31 square units

Therefore, the area of the polygon is 31 square units.