PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 15 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 = 19.
(a)
Length TS
= 15 - 8
= 7 cm
Length NT =
u cm (Isosceles triangle)
Length SP
= Length CG
= (
u + 7) cm (Isosceles triangle)
Length LQ
=
u +
u + 7
= (2
u + 7) cm
(b)
Area of Rectangle LMRT
= 19 x 15
= 285 cm
2 Length RQ
=
u + 7
= 19 + 7
= 26 cm
Area of Rectangle PQRS
= 26 x 8
= 208 cm
2 Area of Triangle MNT
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle NPS
=
12 x 26 x 26
= 338 cm
2 Total area of the figure
= 285 + 208 + 180.5 + 338
= 1011.5 cm
2 Answer(s): (a) (2
u + 7) cm; b) 1011.5 cm
2