PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 18 cm, GH = 10 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 = 19.
(a)
Length LK
= 18 - 10
= 8 cm
Length FL =
m cm (Isosceles triangle)
Length KG
= Length CG
= (
m + 8) cm (Isosceles triangle)
Length DH
=
m +
m + 8
= (2
m + 8) cm
(b)
Area of Rectangle DEJL
= 19 x 18
= 342 cm
2 Length JH
=
m + 8
= 19 + 8
= 27 cm
Area of Rectangle GHJK
= 27 x 10
= 270 cm
2 Area of Triangle EFL
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle FGK
=
12 x 27 x 27
= 364.5 cm
2 Total area of the figure
= 342 + 270 + 180.5 + 364.5
= 1157 cm
2 Answer(s): (a) (2
m + 8) cm; b) 1157 cm
2