There is a circle with a centre T and a radius of 8 cm.

Solution

In the right-angled triangle TEK: TE = Radius = 8 cm KT = Hypotenuse = 17 cm Using Pythagoras theorem: ⇒ KE² = KT² - TE² ⇒ KE² = 17² - 8² ⇒ KE² = 289 - 64 ⇒ KE² = 225 ⇒ KE = √225 ⇒ KE = 15 cm Area of Triangle TEK: ⇒ Area = (1/2) × TE × KE ⇒ Area = (1/2) × 8 × 15 ⇒ Area = 60 sq.cm Since TEKI is symmetrical: Area of Quadrilateral TEKI = 2 × Area of Triangle TEK ⇒ Area of TEKI = 2 × 60 ⇒ Area of TEKI = 120 sq.cm The area of the quadrilateral TEKI is 120 sq.cm.