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Answer :
The area of the triangle is 8 cm². The area of the segment is (4π − 8) cm².
Given the radius (r) is 4 cm and the central angle (θ) is 90°, the area of the sector can be calculated using:
Area of sector = (θ/360) * π * r²
Area of sector = (90/360) * π * 4²
Area of sector = (1/4) * π * 16
Area of sector = 4π cm²
The triangle formed by the radii and the chord is a right triangle (90° angle). The two radii are the legs of the right triangle, each with a length of 4 cm. The area of the right triangle is:
Area of triangle = 1/2 * base * height
Area of triangle = 1/2 * 4 * 4
Area of triangle = 8 cm²
The area of the segment is the area of the sector minus the area of the triangle:
Area of segment = Area of sector - Area of triangle
Area of segment = 4π - 8 cm²
Note the complete question is:
Circle O is shown. Two radii with a length of 4 centimeters are drawn. A chord is drawn from the radii point on the circle to form a triangle. The space between the triangle and the circle is shaded. The radius of the circle is 4 cm and the measure of the central angle is 90°. The area of the sector with a central angle measuring 90° and radius of length 4 cm is π cm². The triangle in the sector is a right triangle. The area of the triangle is cm². The area of the segment of the circle is (4π − ) cm².
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Rewritten by : Jeany
