PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 8 cm, PQ = 4 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 = 15.
(a)
Length TS
= 8 - 4
= 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
= 15 x 8
= 120 cm
2 Length RQ
=
u + 4
= 15 + 4
= 19 cm
Area of Rectangle PQRS
= 19 x 4
= 76 cm
2 Area of Triangle MNT
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle NPS
=
12 x 19 x 19
= 180.5 cm
2 Total area of the figure
= 120 + 76 + 112.5 + 180.5
= 489 cm
2 Answer(s): (a) (2
u + 4) cm; b) 489 cm
2