PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 9 cm, QR = 5 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 = 12.
(a)
Length UT
= 9 - 5
= 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
= 12 x 9
= 108 cm
2 Length SR
=
v + 4
= 12 + 4
= 16 cm
Area of Rectangle QRST
= 16 x 5
= 80 cm
2 Area of Triangle NPU
=
12 x 12 x 12
= 72 cm
2 Area of Triangle PQT
=
12 x 16 x 16
= 128 cm
2 Total area of the figure
= 108 + 80 + 72 + 128
= 388 cm
2 Answer(s): (a) (2
v + 4) cm; b) 388 cm
2