10.2.5 Perimeter and Area, PT3 Practice - Mathematics

Question 12:
Diagram shows a quadrant KLM with centre M and sector JMN with centre J.

Using

π = 22 7 , calculate

(a) the perimeter, in cm, of the whole diagram,

(b) the area, in cm², of the shaded region.

[6 marks]

Solution:

(a)

KM² = JK² + JM²

KM²= 3²+ 4²

KM²= 25

KM= 5 cm

Perimeter of the whole diagram

= NJ + JK + KL+ LM + MN

= 4 + 3 + ( 1 4 × 2 × 22 7 × 5 ) + 5 + ( 30 360 × 2 × 22 7 × 4 ) = 7 + ( 55 7 ) + 5 + ( 44 21 ) = 21 20 21 c m

(b)

Area of the shaded region

= Area of KLM + Area of JMN

= ( 1 4 × 22 7 × 5 2 ) + ( 30 360 × 22 7 × 4 2 ) = 274 14 + 88 21 = 23 16 21 c m 2