PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 10 cm, GH = 6 cm and EL =
m cm. DJH and FLKJ are straight lines.
- Find the length of DH in terms of m. Give your answer in the simplest form.
- Find the total area of the figure when m = 20.
(a)
Length LK
= 10 - 6
= 4 cm
Length FL =
m cm (Isosceles triangle)
Length KG
= Length CG
= (
m + 4) cm (Isosceles triangle)
Length DH
=
m +
m + 4
= (2
m + 4) cm
(b)
Area of Rectangle DEJL
= 20 x 10
= 200 cm
2 Length JH
=
m + 4
= 20 + 4
= 24 cm
Area of Rectangle GHJK
= 24 x 6
= 144 cm
2 Area of Triangle EFL
=
12 x 20 x 20
= 200 cm
2 Area of Triangle FGK
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 200 + 144 + 200 + 288
= 832 cm
2 Answer(s): (a) (2
m + 4) cm; b) 832 cm
2