PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 9 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 = 15.
(a)
Length UT
= 9 - 5
= 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
= 15 x 9
= 135 cm
2 Length SR
=
v + 4
= 15 + 4
= 19 cm
Area of Rectangle QRST
= 19 x 5
= 95 cm
2 Area of Triangle NPU
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle PQT
=
12 x 19 x 19
= 180.5 cm
2 Total area of the figure
= 135 + 95 + 112.5 + 180.5
= 523 cm
2 Answer(s): (a) (2
v + 4) cm; b) 523 cm
2