PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 13 cm, QR = 8 cm and NU =
v cm. MSR and PUTS are straight lines.
- Find the length of MR in terms of v. Give your answer in the simplest form.
- Find the total area of the figure when v = 15.
(a)
Length UT
= 13 - 8
= 5 cm
Length PU =
v cm (Isosceles triangle)
Length TQ
= Length CG
= (
v + 5) cm (Isosceles triangle)
Length MR
=
v +
v + 5
= (2
v + 5) cm
(b)
Area of Rectangle MNSU
= 15 x 13
= 195 cm
2 Length SR
=
v + 5
= 15 + 5
= 20 cm
Area of Rectangle QRST
= 20 x 8
= 160 cm
2 Area of Triangle NPU
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle PQT
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 195 + 160 + 112.5 + 200
= 667.5 cm
2 Answer(s): (a) (2
v + 5) cm; b) 667.5 cm
2