PSLEThe figure is made up of two rectangles, KLSQ and QRNP, and two right-angled isosceles triangles, LMS and NMR. LK = 9 cm, NP = 5 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 = 13.
(a)
Length SR
= 9 - 5
= 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
= 13 x 9
= 117 cm
2 Length QP
=
t + 4
= 13 + 4
= 17 cm
Area of Rectangle NPQR
= 17 x 5
= 85 cm
2 Area of Triangle LMS
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle MNR
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 117 + 85 + 84.5 + 144.5
= 431 cm
2 Answer(s): (a) (2
t + 4) cm; b) 431 cm
2