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A circle is drawn within a square as shown.

What is the best approximation for the area of the shaded region?

Use 3.14 to approximate pi.

168.56 in²

696.08 in²

740.04 in²

1677.76 in²

A circle is drawn within a square as shown. What is the best approximation for the-example-1
User Spullen
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6.1k points

2 Answers

5 votes

Answer:

A ≈ 168.56 in²

Explanation:

i took the test :D

User Matt Mazzola
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6.3k points
4 votes

As it is shown in the figure, the length of the square's side s is also the length of the circle's diameter d:

s = d = 28 in.


• Computing the area of the square:

A₁ = s²

A₁ = 28²

A₁ = 28 × 28

A₁ = 784 in²


• Computing the area of the circle:

A₂ = π × r²

A₂ = π × (d/2)²

A₂ = π × (28/2)²

A₂ = π × 14²

A₂ ≈ 3.14 × 14 × 14

A₂ ≈ 615.44 in²

—————

• The area of the shaded portion is equal to the difference between the area of the square and the area of circle:

A = A₁ – A₂

A ≈ 784 – 615.44

A 168.56 in² <——— this is the answer (1st option).


I hope this helps. =)

User Aarti
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6.3k points