PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 9 cm, GH = 4 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
= 9 - 4
= 5 cm
Length FL =
m cm (Isosceles triangle)
Length KG
= Length CG
= (
m + 5) cm (Isosceles triangle)
Length DH
=
m +
m + 5
= (2
m + 5) cm
(b)
Area of Rectangle DEJL
= 20 x 9
= 180 cm
2 Length JH
=
m + 5
= 20 + 5
= 25 cm
Area of Rectangle GHJK
= 25 x 4
= 100 cm
2 Area of Triangle EFL
=
12 x 20 x 20
= 200 cm
2 Area of Triangle FGK
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 180 + 100 + 200 + 312.5
= 792.5 cm
2 Answer(s): (a) (2
m + 5) cm; b) 792.5 cm
2