PSLEThe figure is made up of two rectangles, KLSQ and QRNP, and two right-angled isosceles triangles, LMS and NMR. LK = 15 cm, NP = 8 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 = 18.
(a)
Length SR
= 15 - 8
= 7 cm
Length MS =
t cm (Isosceles triangle)
Length RN
= Length CG
= (
t + 7) cm (Isosceles triangle)
Length KP
=
t +
t + 7
= (2
t + 7) cm
(b)
Area of Rectangle KLQS
= 18 x 15
= 270 cm
2 Length QP
=
t + 7
= 18 + 7
= 25 cm
Area of Rectangle NPQR
= 25 x 8
= 200 cm
2 Area of Triangle LMS
=
12 x 18 x 18
= 162 cm
2 Area of Triangle MNR
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 270 + 200 + 162 + 312.5
= 944.5 cm
2 Answer(s): (a) (2
t + 7) cm; b) 944.5 cm
2