PSLEThe figure is made up of two rectangles, DELJ and JKGH, and two right-angled isosceles triangles, EFL and GFK. ED = 13 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
= 13 - 7
= 6 cm
Length FL =
m cm (Isosceles triangle)
Length KG
= Length CG
= (
m + 6) cm (Isosceles triangle)
Length DH
=
m +
m + 6
= (2
m + 6) cm
(b)
Area of Rectangle DEJL
= 17 x 13
= 221 cm
2 Length JH
=
m + 6
= 17 + 6
= 23 cm
Area of Rectangle GHJK
= 23 x 7
= 161 cm
2 Area of Triangle EFL
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle FGK
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 221 + 161 + 144.5 + 264.5
= 791 cm
2 Answer(s): (a) (2
m + 6) cm; b) 791 cm
2