PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 14 cm, PQ = 9 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 = 18.
(a)
Length TS
= 14 - 9
= 5 cm
Length NT =
u cm (Isosceles triangle)
Length SP
= Length CG
= (
u + 5) cm (Isosceles triangle)
Length LQ
=
u +
u + 5
= (2
u + 5) cm
(b)
Area of Rectangle LMRT
= 18 x 14
= 252 cm
2 Length RQ
=
u + 5
= 18 + 5
= 23 cm
Area of Rectangle PQRS
= 23 x 9
= 207 cm
2 Area of Triangle MNT
=
12 x 18 x 18
= 162 cm
2 Area of Triangle NPS
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 252 + 207 + 162 + 264.5
= 885.5 cm
2 Answer(s): (a) (2
u + 5) cm; b) 885.5 cm
2