PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 14 cm, QR = 8 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 = 20.
(a)
Length UT
= 14 - 8
= 6 cm
Length PU =
v cm (Isosceles triangle)
Length TQ
= Length CG
= (
v + 6) cm (Isosceles triangle)
Length MR
=
v +
v + 6
= (2
v + 6) cm
(b)
Area of Rectangle MNSU
= 20 x 14
= 280 cm
2 Length SR
=
v + 6
= 20 + 6
= 26 cm
Area of Rectangle QRST
= 26 x 8
= 208 cm
2 Area of Triangle NPU
=
12 x 20 x 20
= 200 cm
2 Area of Triangle PQT
=
12 x 26 x 26
= 338 cm
2 Total area of the figure
= 280 + 208 + 200 + 338
= 1026 cm
2 Answer(s): (a) (2
v + 6) cm; b) 1026 cm
2