PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 12 cm, QR = 7 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 = 16.
(a)
Length UT
= 12 - 7
= 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
= 16 x 12
= 192 cm
2 Length SR
=
v + 5
= 16 + 5
= 21 cm
Area of Rectangle QRST
= 21 x 7
= 147 cm
2 Area of Triangle NPU
=
12 x 16 x 16
= 128 cm
2 Area of Triangle PQT
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 192 + 147 + 128 + 220.5
= 687.5 cm
2 Answer(s): (a) (2
v + 5) cm; b) 687.5 cm
2