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 = 20.
(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
= 20 x 8
= 160 cm
2 Length JH
=
m + 3
= 20 + 3
= 23 cm
Area of Rectangle GHJK
= 23 x 5
= 115 cm
2 Area of Triangle EFL
=
12 x 20 x 20
= 200 cm
2 Area of Triangle FGK
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 160 + 115 + 200 + 264.5
= 739.5 cm
2 Answer(s): (a) (2
m + 3) cm; b) 739.5 cm
2