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Semicircles are constructed on the three sides of a triangle as shown below. Find the area of the shaded region.

Semicircles are constructed on the three sides of a triangle as shown below. Find-example-1
User Blackdrag
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Answer:

approximately 157 square units

Explanation:

To find areas of all shaded regions, find the area of each of the three triangles

Area of circle with diameter of 6, radius of 3 is:

A = π3² = 9π

Area of circle with diameter of 8, radius of 4 is:

A = π4² = 16π

Area of circle with diameter of 10*, radius of 5 is:

A = π5² = 25π

*Found this value by using the Pythagorean Theorem for the right triangle

Total Area = 50π which is approximately 157 square units

User Joscplan
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