PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 8 cm, GH = 5 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 = 14.
(a)
Length LK
= 8 - 5
= 3 cm
Length FL =
m cm (Isosceles triangle)
Length KG
= Length CG
= (
m + 3) cm (Isosceles triangle)
Length DH
=
m +
m + 3
= (2
m + 3) cm
(b)
Area of Rectangle DEJL
= 14 x 8
= 112 cm
2 Length JH
=
m + 3
= 14 + 3
= 17 cm
Area of Rectangle GHJK
= 17 x 5
= 85 cm
2 Area of Triangle EFL
=
12 x 14 x 14
= 98 cm
2 Area of Triangle FGK
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 112 + 85 + 98 + 144.5
= 439.5 cm
2 Answer(s): (a) (2
m + 3) cm; b) 439.5 cm
2