The diagonal of the square inscribed in the circle below is 8cm. Find the shaded area. (Use pi = 3.14)
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.
Since the height of the triangle is the radius of the circle, it is therefore ½(8) = 4cm.
(1) Area of the Circle ()
The formula for finding the area of a circle is
where r is the radius.
Substituting the 4 cm to radius, we have
(2) Area of the Square ()
To find the area of the square, we can first find the area of the triangle. To find the area of triangle ABC, we have
where b is the base and h is the height.
Substituting we have
Since there are two triangles, each with area 16 sq. cm, the area of the whole square is
(3) Shaded area
shaded area = area the circle – area of the square
shaded area = 50.24 – 32
shaded area = 18.24
Answer: 18.24 sq.cm