PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 11 cm, GH = 6 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 = 16.
(a)
Length LK
= 11 - 6
= 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
= 16 x 11
= 176 cm
2 Length JH
=
m + 5
= 16 + 5
= 21 cm
Area of Rectangle GHJK
= 21 x 6
= 126 cm
2 Area of Triangle EFL
=
12 x 16 x 16
= 128 cm
2 Area of Triangle FGK
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 176 + 126 + 128 + 220.5
= 650.5 cm
2 Answer(s): (a) (2
m + 5) cm; b) 650.5 cm
2