PSLEThe figure is made up of two rectangles, KLSQ and QRNP, and two right-angled isosceles triangles, LMS and NMR. LK = 14 cm, NP = 9 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 = 17.
(a)
Length SR
= 14 - 9
= 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
= 17 x 14
= 238 cm
2 Length QP
=
t + 5
= 17 + 5
= 22 cm
Area of Rectangle NPQR
= 22 x 9
= 198 cm
2 Area of Triangle LMS
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle MNR
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 238 + 198 + 144.5 + 242
= 822.5 cm
2 Answer(s): (a) (2
t + 5) cm; b) 822.5 cm
2