Question

Calculate the area of trapezium CDEF. Please show the working out

Answer 1

A rectangle is a parallelogram, and parallelograms have opposite congruent sides. So CF = AB, which is 6 cm. Now we know the height of the trapezium.

The perimeter of a rectangle is 2L + 2W = P, where L is the length, W is the width, and P is the perimeter. Since you know that 6 is one of the side lengths and the perimeter is 20, plug it is for one of the variables and solve.
Ex: 2(6) + 2W = 20
12 + 2W = 20
2W = 8
W = 4.
So, the length of the other two sides is 4 cm wide.

The formula for the area of the trapezium is A = 1/2 * h * (b1 + b2), where h is the height, or altitude of the trapezium, and b1 and b2 are the base lengths.
Plug in the information you gathered into the formula:
A = 1/2 (6)(3+4)
A = 1/2 (6)(7)
A = 21

The area of trapezium CDEF is 21 cm^2 (cm squared).

Although the lengths may not seem appropriate due to the image given, remember that the diagram is not drawn to scale, as stated in the top right corner. 

Hope this helps!

Answer 2

Answer: 24cm²

Step-by-step explanation: From the given sides, we would try to find the unknown sides.

If abcf is a rectangle, then ba = fc and fa = cb

Which implies that:

ba = fc = 6cm

If Perimeter of abcf = 20cm

And fa = bc;

Then fa = cb = [ 20 - (ba + fc) ] / 2

= (20 - (6 + 6) ] / 2

= (20 - 12) / 2

= 8/2 = 4cm

If cb = 4cm and bd = 9cm;

Then dc = 9 - 4 = 5cm

Height of trapezium is equal to ba = fc (alternatively you can get it by measuring out 3cm from point C towards D, then draw a perpendicular line to point E) = 6cm

Parallel sides of trapezium are dc = 5cm and fe = 3cm

Area of trapezium is given by half sum of parallel side multiplied by height = (5 + 3)/2 x 6

Area = (8/2) x 6 = 4 x 6 = 24cm²

Area of trapezium is 24cm²