PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 7 cm, QR = 4 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
= 7 - 4
= 3 cm
Length PU =
v cm (Isosceles triangle)
Length TQ
= Length CG
= (
v + 3) cm (Isosceles triangle)
Length MR
=
v +
v + 3
= (2
v + 3) cm
(b)
Area of Rectangle MNSU
= 15 x 7
= 105 cm
2 Length SR
=
v + 3
= 15 + 3
= 18 cm
Area of Rectangle QRST
= 18 x 4
= 72 cm
2 Area of Triangle NPU
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle PQT
=
12 x 18 x 18
= 162 cm
2 Total area of the figure
= 105 + 72 + 112.5 + 162
= 451.5 cm
2 Answer(s): (a) (2
v + 3) cm; b) 451.5 cm
2