Question

In the diagram shown,

ABCE is a trapezium,
AD is parallel to BC,
DE = 4 cm,
Area of ABCE = 60 cm?,
Area of ABCD = 48 cm?.
g cm
Work out the values of fand g.
You must show all your working.
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Answer 1

area of ABCE= 60cm²

area of ABCD= 48cm²

BA is parallel to CD

f cm= 48÷4

f cm=12cm

area of ADE= 12×4÷2

area of ADE=24cm²

Explanation:

Answer 2

The values of f and g are;

f = 6

f = 6g = 8

We are given the trapezium ABCE where;

AD is parallel to BC

DE = 4 cm

Area of ABCE = 60 cm²

Area of ABCD = 48 cm²

f and g are sides of the rectangle ABCD.

fg = 48 - - - (eq 1)

Also,for the trapezium ABCE;

½(g + g + 4)f = 60

(2g + 4)f = 120 - - - (eq 2)

From eq 1, f = 48/g

(2g + 4) × (48/g) = 120

96 + 192/g = 120

192/g = 120 - 96

192/g = 24

g = 192/24

g = 8

8f = 48

f = 48/8

f = 6