PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 13 cm, PQ = 8 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 = 16.
(a)
Length TS
= 13 - 8
= 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
= 16 x 13
= 208 cm
2 Length RQ
=
u + 5
= 16 + 5
= 21 cm
Area of Rectangle PQRS
= 21 x 8
= 168 cm
2 Area of Triangle MNT
=
12 x 16 x 16
= 128 cm
2 Area of Triangle NPS
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 208 + 168 + 128 + 220.5
= 724.5 cm
2 Answer(s): (a) (2
u + 5) cm; b) 724.5 cm
2