In the circle illustrated, the circumference...

Question 1 of 270705eccef9dbacbc34ba4d45deb

In the circle illustrated, the circumference is 50.24 feet. What is the area of the shaded portion? See illustration GS-0134.

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Question 1 of 27070

Q

In the circle illustrated, the circumference is 50.24 feet. What is the area of the shaded portion? See illustration GS-0134.

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🔍 Key Concepts

• Use the circle’s circumference to find its radius first using the formula C = 2πR. • Notice the shaded region is a circular segment formed by a sector minus a right triangle inside the circle. • Area of shaded region = (area of the sector) − (area of the right triangle).

💭 Think About

• What is the radius if the circumference is 50.24 feet and you use π ≈ 3.14? • What fraction of the full circle is represented by the central right angle shown (the little square)? • Once you know that fraction, what is the area of the corresponding sector, and how does the area of the right triangle with legs equal to the radius compare?

✅ Before You Answer

• Be sure you correctly compute R from C using $C = 2\pi R$ . • Confirm what portion of 360° the central right angle represents before finding the sector area. • Carefully subtract triangle area from sector area and keep units in square feet.