PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 7 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 = 12.
(a)
Length LK
= 7 - 4
= 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
= 12 x 7
= 84 cm
2 Length JH
=
m + 3
= 12 + 3
= 15 cm
Area of Rectangle GHJK
= 15 x 4
= 60 cm
2 Area of Triangle EFL
=
12 x 12 x 12
= 72 cm
2 Area of Triangle FGK
=
12 x 15 x 15
= 112.5 cm
2 Total area of the figure
= 84 + 60 + 72 + 112.5
= 328.5 cm
2 Answer(s): (a) (2
m + 3) cm; b) 328.5 cm
2