PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 8 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 = 11.
(a)
Length UT
= 8 - 4
= 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
= 11 x 8
= 88 cm
2 Length SR
=
v + 4
= 11 + 4
= 15 cm
Area of Rectangle QRST
= 15 x 4
= 60 cm
2 Area of Triangle NPU
=
12 x 11 x 11
= 60.5 cm
2 Area of Triangle PQT
=
12 x 15 x 15
= 112.5 cm
2 Total area of the figure
= 88 + 60 + 60.5 + 112.5
= 321 cm
2 Answer(s): (a) (2
v + 4) cm; b) 321 cm
2