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 = 17.
(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
= 17 x 14
= 238 cm
2 Length RQ
=
u + 5
= 17 + 5
= 22 cm
Area of Rectangle PQRS
= 22 x 9
= 198 cm
2 Area of Triangle MNT
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle NPS
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 238 + 198 + 144.5 + 242
= 822.5 cm
2 Answer(s): (a) (2
u + 5) cm; b) 822.5 cm
2