PSLEThe figure is made up of two rectangles, KLSQ and QRNP, and two right-angled isosceles triangles, LMS and NMR. LK = 8 cm, NP = 4 cm and LS =
t cm. KQP and MSRQ are straight lines.
- Find the length of KP in terms of t. Give your answer in the simplest form.
- Find the total area of the figure when t = 14.
(a)
Length SR
= 8 - 4
= 4 cm
Length MS =
t cm (Isosceles triangle)
Length RN
= Length CG
= (
t + 4) cm (Isosceles triangle)
Length KP
=
t +
t + 4
= (2
t + 4) cm
(b)
Area of Rectangle KLQS
= 14 x 8
= 112 cm
2 Length QP
=
t + 4
= 14 + 4
= 18 cm
Area of Rectangle NPQR
= 18 x 4
= 72 cm
2 Area of Triangle LMS
=
12 x 14 x 14
= 98 cm
2 Area of Triangle MNR
=
12 x 18 x 18
= 162 cm
2 Total area of the figure
= 112 + 72 + 98 + 162
= 444 cm
2 Answer(s): (a) (2
t + 4) cm; b) 444 cm
2