PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 12 cm, QR = 7 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 = 14.
(a)
Length UT
= 12 - 7
= 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
= 14 x 12
= 168 cm
2 Length SR
=
v + 5
= 14 + 5
= 19 cm
Area of Rectangle QRST
= 19 x 7
= 133 cm
2 Area of Triangle NPU
=
12 x 14 x 14
= 98 cm
2 Area of Triangle PQT
=
12 x 19 x 19
= 180.5 cm
2 Total area of the figure
= 168 + 133 + 98 + 180.5
= 579.5 cm
2 Answer(s): (a) (2
v + 5) cm; b) 579.5 cm
2