Question

The polygons are regular polygons. What is the area of the shaded region to the nearest tenth? (see attachment)

Answer 1

if 4in. is length of that line connecting the lower-left corners, then the main diagonal of the large square is 8, and the main diagonal of the small square is 4. Use the formula for area of a rhombus to find the area of each square, then subtract areas.

Answer 2

The larger square has diagonal length 8. The diagonals of a square are congruent.
The area of a square can be found by taking one-half the product of its diagonals.
The area of the larger square is (1/2) 8*8 = 32.
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The area of the smaller square can be found in a likewise manner:
Area = (1/2) 4*4 = 8
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Area of shaded region = 32 - 8 = 24.0