PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 10 cm, QR = 6 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 = 13.
(a)
Length UT
= 10 - 6
= 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
= 13 x 10
= 130 cm
2 Length SR
=
v + 4
= 13 + 4
= 17 cm
Area of Rectangle QRST
= 17 x 6
= 102 cm
2 Area of Triangle NPU
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle PQT
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 130 + 102 + 84.5 + 144.5
= 461 cm
2 Answer(s): (a) (2
v + 4) cm; b) 461 cm
2