PSLEThe figure is made up of two rectangles, LMTR and RSPQ, and two right-angled isosceles triangles, MNT and PNS. ML = 13 cm, PQ = 7 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
= 13 - 7
= 6 cm
Length NT =
u cm (Isosceles triangle)
Length SP
= Length CG
= (
u + 6) cm (Isosceles triangle)
Length LQ
=
u +
u + 6
= (2
u + 6) cm
(b)
Area of Rectangle LMRT
= 19 x 13
= 247 cm
2 Length RQ
=
u + 6
= 19 + 6
= 25 cm
Area of Rectangle PQRS
= 25 x 7
= 175 cm
2 Area of Triangle MNT
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle NPS
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 247 + 175 + 180.5 + 312.5
= 915 cm
2 Answer(s): (a) (2
u + 6) cm; b) 915 cm
2