The diagram below shows a square inside a regular octagon. The apothem of the octagon is 15.69 units. To the nearest square unit
, what is the area of the shaded region? Apothem length: 15.69 A. 1463 square units B. 764 square units C. 647 square units D. 816 square units
2 answers:
I found the image of this problem. Its side measure is 13. The octagon can form 8 triangles. Its apothem can serve as the height of the triangle. We need to get the area of the triangle and multiply it by 8. We then deduct the area of the square from the total area.
Area of a triangle = (height * base) / 2
A = (15.69 * 13) / 2
A = 203.97 / 2
A = 101.985 sq. units
101.985 x 8 = 815.88 sq. units
Area of the square = s²
A = 13²
A = 169 sq. unit
Area of the shaded region: 815.88 sq. unit - 169 sq. unit = 646.88 sq. unit
Area of a triangle = (height * base) / 2
A = (15.69 * 13) / 2
A = 203.97 / 2
A = 101.985 sq. units
101.985 x 8 = 815.88 sq. units
Area of the square = s²
A = 13²
A = 169 sq. unit
Area of the shaded region: 815.88 sq. unit - 169 sq. unit = 646.88 sq. unit
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