Question

How can you prove that the total area of the two shaded lunes (moon shapes) is equal to the area of the triangle?

A. By using the Pythagorean theorem
B. By applying the area of a circle formula
C. By using the sector area formula
D. By calculating the base and height of the triangle

Answer 1

The total area of the two shaded lunes can be proven to be equal to the area of the triangle by using the sector area formula.

The total area of the two shaded lunes can be proven to be equal to the area of the triangle by using the sector area formula. The sector area formula states that the area of a sector of a circle can be found by multiplying half the angle (in radians) by the square of the radius. Since the two shaded lunes are congruent to each other and have the same angle, their combined area is equal to the area of the sector formed by the angle at C. And since the triangle ABC is formed by the same angle as the shaded lunes, the area of the triangle is also equal to the area of the sector.

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