PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 11 cm, GH = 7 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 = 17.
(a)
Length LK
= 11 - 7
= 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
= 17 x 11
= 187 cm
2 Length JH
=
m + 4
= 17 + 4
= 21 cm
Area of Rectangle GHJK
= 21 x 7
= 147 cm
2 Area of Triangle EFL
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle FGK
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 187 + 147 + 144.5 + 220.5
= 699 cm
2 Answer(s): (a) (2
m + 4) cm; b) 699 cm
2