PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 10 cm, QR = 6 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 = 18.
(a)
Length UT
= 10 - 6
= 4 cm
Length PU =
v cm (Isosceles triangle)
Length TQ
= Length CG
= (
v + 4) cm (Isosceles triangle)
Length MR
=
v +
v + 4
= (2
v + 4) cm
(b)
Area of Rectangle MNSU
= 18 x 10
= 180 cm
2 Length SR
=
v + 4
= 18 + 4
= 22 cm
Area of Rectangle QRST
= 22 x 6
= 132 cm
2 Area of Triangle NPU
=
12 x 18 x 18
= 162 cm
2 Area of Triangle PQT
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 180 + 132 + 162 + 242
= 716 cm
2 Answer(s): (a) (2
v + 4) cm; b) 716 cm
2