PSLEThe figure is made up of two rectangles, KLSQ and QRNP, and two right-angled isosceles triangles, LMS and NMR. LK = 9 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 = 16.
(a)
Length SR
= 9 - 4
= 5 cm
Length MS =
t cm (Isosceles triangle)
Length RN
= Length CG
= (
t + 5) cm (Isosceles triangle)
Length KP
=
t +
t + 5
= (2
t + 5) cm
(b)
Area of Rectangle KLQS
= 16 x 9
= 144 cm
2 Length QP
=
t + 5
= 16 + 5
= 21 cm
Area of Rectangle NPQR
= 21 x 4
= 84 cm
2 Area of Triangle LMS
=
12 x 16 x 16
= 128 cm
2 Area of Triangle MNR
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 144 + 84 + 128 + 220.5
= 576.5 cm
2 Answer(s): (a) (2
t + 5) cm; b) 576.5 cm
2