Question

A pentagon is shown. Two circles and a triangle are cut out of the pentagon. Two triangles are attached to the top two corners of the pentagon.
What are the steps you would take to find the area of the shaded region? Check all that apply.

Identify the shapes you will need to determine the area of the figure.
Calculate and add the areas of the regular pentagon and two orange triangles.
Calculate and add the areas of the unshaded triangle and two circles.
Subtract the sum of the unshaded triangle and circles from the sum of the regular pentagon and two orange triangles.

Answer 1

All of them. Steps to find the shaded area:

1. Identify the component shapes (regular pentagon, two attached small triangles, one removed triangle, two removed circles).
2. Compute and add the areas of the big composite shape (regular pentagon + the two orange triangles).
3. Compute and add the areas of the removed parts (the unshaded triangle + the two circles).
4. Subtract the total area of the removed parts from the total area of the big composite shape to get the shaded area.