PSLEThe figure is made up of two rectangles, KLSQ and QRNP, and two right-angled isosceles triangles, LMS and NMR. LK = 11 cm, NP = 6 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 = 20.
(a)
Length SR
= 11 - 6
= 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
= 20 x 11
= 220 cm
2 Length QP
=
t + 5
= 20 + 5
= 25 cm
Area of Rectangle NPQR
= 25 x 6
= 150 cm
2 Area of Triangle LMS
=
12 x 20 x 20
= 200 cm
2 Area of Triangle MNR
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 220 + 150 + 200 + 312.5
= 882.5 cm
2 Answer(s): (a) (2
t + 5) cm; b) 882.5 cm
2