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 = 10.
(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
= 10 x 7
= 70 cm
2 Length JH
=
m + 3
= 10 + 3
= 13 cm
Area of Rectangle GHJK
= 13 x 4
= 52 cm
2 Area of Triangle EFL
=
12 x 10 x 10
= 50 cm
2 Area of Triangle FGK
=
12 x 13 x 13
= 84.5 cm
2 Total area of the figure
= 70 + 52 + 50 + 84.5
= 256.5 cm
2 Answer(s): (a) (2
m + 3) cm; b) 256.5 cm
2