PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 10 cm, QR = 5 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 - 5
= 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
= 13 x 10
= 130 cm
2 Length SR
=
v + 5
= 13 + 5
= 18 cm
Area of Rectangle QRST
= 18 x 5
= 90 cm
2 Area of Triangle NPU
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle PQT
=
12 x 18 x 18
= 162 cm
2 Total area of the figure
= 130 + 90 + 84.5 + 162
= 466.5 cm
2 Answer(s): (a) (2
v + 5) cm; b) 466.5 cm
2