PSLEThe figure is made up of two rectangles, MNUS and STQR, and two right-angled isosceles triangles, NPU and QPT. NM = 13 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 = 19.
(a)
Length UT
= 13 - 7
= 6 cm
Length PU =
v cm (Isosceles triangle)
Length TQ
= Length CG
= (
v + 6) cm (Isosceles triangle)
Length MR
=
v +
v + 6
= (2
v + 6) cm
(b)
Area of Rectangle MNSU
= 19 x 13
= 247 cm
2 Length SR
=
v + 6
= 19 + 6
= 25 cm
Area of Rectangle QRST
= 25 x 7
= 175 cm
2 Area of Triangle NPU
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle PQT
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 247 + 175 + 180.5 + 312.5
= 915 cm
2 Answer(s): (a) (2
v + 6) cm; b) 915 cm
2