Shaded Area – Right Triangle Inscribed in a Circle

A right triangle is inscribed in a circle such that its longest side is the diameter of the circle. If the shorter sides of the triangle measure 6cm and 8cm, find the area of the shaded region. Use \pi = 3.14

Solution

A triangle inscribed in a circle with its longest side as the diameter of the circle is always a right triangle (by Thales’ Theorem). So, we can find the area A_T of the triangle.

right triangle inscribed in a circle

Finding the area of the triangle,

A_T = \frac{6 \times 8}{2} = 24Continue reading “Shaded Area – Right Triangle Inscribed in a Circle”

Shaded Area – Square Inscribed in a Circle

The diagonal of the square inscribed in the circle below is 8cm. Find the shaded area. (Use pi = 3.14)

square inscribed in a circle

 

 

 

 

 

 

 

Solution

From the diagram above, we can get the shaded area by subtracting the area of the square from the area of the circle.

We let the diagonal of the square be the base of two the triangles. Next, we draw the height of one of the triangles. Continue reading “Shaded Area – Square Inscribed in a Circle”