Question

Circle O is shown. 2 radii with length 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
.

The area of the triangle is
cm2.

The area of the segment of the circle is
(4π −
) cm2.

Answer 1

Sector area = (90/360)·π·4^2 = 4π cm^2.

The triangle in the sector is an isosceles right triangle (two radii meet at a 90° angle).

Triangle area = (1/2)·4·4 = 8 cm^2.

Segment area = sector − triangle = 4π − 8 cm^2.