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 = 18.
(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
= 18 x 9
= 162 cm
2 Length JH
=
m + 5
= 18 + 5
= 23 cm
Area of Rectangle GHJK
= 23 x 4
= 92 cm
2 Area of Triangle EFL
=
12 x 18 x 18
= 162 cm
2 Area of Triangle FGK
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 162 + 92 + 162 + 264.5
= 680.5 cm
2 Answer(s): (a) (2
m + 5) cm; b) 680.5 cm
2