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3 years ago

△ABC is a right isosceles triangle, the centers of two arcs are the midpoint of AB

Mathematics

1 answer:

mel-nik [20]3 years ago

4 0

Answer:

Step-by-step explanation:

Let's define 3 areas:

S = area of semicircle with radius 6 in (diameter AB)
T = area of quarter circle with radius 6√2 in (radius AC)
U = area of triangle ABC (side lengths 6√2)

The white space between the "moon" and the triangle has area ...

white = T - U

Then the area of the "moon" shape is ...

moon = S -white = S -(T -U) = S -T +U

The area we're asked to find is ...

moon - triangle = (S -T +U) -U = S -T

The formula for the area of a circle of radius r is ...

A = πr²

So, ...

S = (1/2)π(6 in)² = 18π in²

and

T = (1/4)π(6√2 in)² = 18π in²

The difference in areas is S -T = (18π in²) -(18π in²) = 0.

There is no difference between the areas of the "moon" and the triangle.

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