PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 9 cm, PQ = 5 cm and MT =
u cm. LRQ and NTSR are straight lines.
- Find the length of LQ in terms of u. Give your answer in the simplest form.
- Find the total area of the figure when u = 10.
(a)
Length TS
= 9 - 5
= 4 cm
Length NT =
u cm (Isosceles triangle)
Length SP
= Length CG
= (
u + 4) cm (Isosceles triangle)
Length LQ
=
u +
u + 4
= (2
u + 4) cm
(b)
Area of Rectangle LMRT
= 10 x 9
= 90 cm
2 Length RQ
=
u + 4
= 10 + 4
= 14 cm
Area of Rectangle PQRS
= 14 x 5
= 70 cm
2 Area of Triangle MNT
=
12 x 10 x 10
= 50 cm
2 Area of Triangle NPS
=
12 x 14 x 14
= 98 cm
2 Total area of the figure
= 90 + 70 + 50 + 98
= 308 cm
2 Answer(s): (a) (2
u + 4) cm; b) 308 cm
2