PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 10 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 = 11.
(a)
Length TS
= 10 - 5
= 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
= 11 x 10
= 110 cm
2 Length RQ
=
u + 5
= 11 + 5
= 16 cm
Area of Rectangle PQRS
= 16 x 5
= 80 cm
2 Area of Triangle MNT
=
12 x 11 x 11
= 60.5 cm
2 Area of Triangle NPS
=
12 x 16 x 16
= 128 cm
2 Total area of the figure
= 110 + 80 + 60.5 + 128
= 378.5 cm
2 Answer(s): (a) (2
u + 5) cm; b) 378.5 cm
2