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A circle is shown. 4 radii are drawn. Chords are drawn to connect the radii points on the circle to form 2 triangles. The triangles have base lengths of 6 centimeters and the other 2 sides have lengths of 5 centimeters. The distance between the base of the triangle to the outline of the circle is 1 centimeter. Everything around the triangles is shaded.
What is the area of the shaded region?
(25π – 48) cm2
(25π – 30) cm2
(25π – 24) cm2
(25π – 12) cm2
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GPT-5 mini
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The two triangles are formed by two radii and a chord, so the circle radius is 5. Circle area = π·5² = 25π.
For one isosceles triangle with sides 5,5 and base 6, the height = sqrt(5² − 3²) = 4, so its area = 1/2·6·4 = 12. Two such triangles have area 24.
Shaded area = circle area − 2·(triangle area) = 25π − 24 cm².
Answer: (25π − 24) cm².
For one isosceles triangle with sides 5,5 and base 6, the height = sqrt(5² − 3²) = 4, so its area = 1/2·6·4 = 12. Two such triangles have area 24.
Shaded area = circle area − 2·(triangle area) = 25π − 24 cm².
Answer: (25π − 24) cm².
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