PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 8 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 = 14.
(a)
Length TS
= 8 - 5
= 3 cm
Length NT =
u cm (Isosceles triangle)
Length SP
= Length CG
= (
u + 3) cm (Isosceles triangle)
Length LQ
=
u +
u + 3
= (2
u + 3) cm
(b)
Area of Rectangle LMRT
= 14 x 8
= 112 cm
2 Length RQ
=
u + 3
= 14 + 3
= 17 cm
Area of Rectangle PQRS
= 17 x 5
= 85 cm
2 Area of Triangle MNT
=
12 x 14 x 14
= 98 cm
2 Area of Triangle NPS
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 112 + 85 + 98 + 144.5
= 439.5 cm
2 Answer(s): (a) (2
u + 3) cm; b) 439.5 cm
2