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Svetach [21]
2 years ago
11

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? 13 U 13 U Apothem length: 15.69 O A. 1463 square units B. 816 square units C. 647 square units OD. 764 square units ​

Mathematics
2 answers:
motikmotik2 years ago
8 0

perimeter of octagon

  • 8(13)
  • 104units

Now area

  • perimeter×apothem /2
  • 104(15.69)/2
  • 52(15.69)
  • 815.88units²

Area of square

  • 13²
  • 169units²

Area of shaded region

  • 815.88-169
  • 646.88units²
  • 647units²
Musya8 [376]2 years ago
3 0

Answer:

C.  647 square units

Step-by-step explanation:

To find the shaded area, subtract the area of the unshaded square from the area of the octagon.

<u>Area of the octagon</u>

\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}

where:

  • n = number of sides
  • l = length of one side
  • a = apothem

Given:

  • n = 8
  • l = 13
  • a = 15.69

Substitute the given values into the formula and solve for A:

\implies \textsf{Area}=\sf \dfrac{8 \cdot 13 \cdot 15.69}{2}

\implies \textsf{Area}=\sf \dfrac{1631.76}{2}

\implies \textsf{Area}=\sf 815.88\:\:square \:units

<u>Area of the square</u>

\implies \textsf{Area}=\sf 13^2=169 \:\:square \:units

<u>Area of the shaded region</u>

= area of the octagon - area of the square

= 815.88 - 169

= 646.88

= 647 square units (nearest square unit)

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