Ai Tong School P6 SA1 2006 Math (Q47)

The figure shown below is made up of a square, a rectangle and a right-angled triangle. The area of the square MNQR is 49 square cm and the area of the rectangle NOPS is 60 square cm. OP is 4 cm.
(a) Find the length of MR
(b) Find the length of SP
(c) Find the area of the triangle PSQ


Solution

(a)
Area of square MNQR = 49 square cm.
1 side is therefore 7 cm (7 x 7 =49)
Answer: 7 cm

(b)
Area of rectangle NOPS is 60 square cm.
60 square cm = SP x 4 cm
SP = 60 square cm divided by 4 cm = 15 cm
Answer: 15 cm

(c)


NQ = 7 cm, therefore
SQ = 7 cm – 4 cm = 3 cm

Area of triangle PSQ = ½ x base x height
= ½ x 15 cm x 3 cm
= 22.5 square cm

Answer: 22.5 square cm