PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 15 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 = 16.
(a)
Length UT
= 15 - 8
= 7 cm
Length PU =
v cm (Isosceles triangle)
Length TQ
= Length CG
= (
v + 7) cm (Isosceles triangle)
Length MR
=
v +
v + 7
= (2
v + 7) cm
(b)
Area of Rectangle MNSU
= 16 x 15
= 240 cm
2 Length SR
=
v + 7
= 16 + 7
= 23 cm
Area of Rectangle QRST
= 23 x 8
= 184 cm
2 Area of Triangle NPU
=
12 x 16 x 16
= 128 cm
2 Area of Triangle PQT
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 240 + 184 + 128 + 264.5
= 816.5 cm
2 Answer(s): (a) (2
v + 7) cm; b) 816.5 cm
2