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Can you work out the perimeter or area of shapes such as a trapezium and a rhombus? The following Math quiz provides a more advanced look at area and perimeters of shapes.

Before trying this quiz, you might want to refresh your memory by playing the easier quiz called 'Level 3-4 Perimeter and Area 01'.

1.

A garden is in the shape of a trapezium and it has an area of 1,500 meters^{2}. One of the parallel sides is 40 meters long and the other parallel side is 60 meters long. What is the distance between the parallel sides?

20 meters

30 meters

40 meters

50 meters

When you are dealing with shapes it is often useful to draw the shape so that you can understand the question better

2.

In many formulas you will see the letter h which stands for 'height'. What would be a more correct term for 'height'?

Perpendicular height

Perpetrator height

Perpetual height

Perplexing height

The perpendicular height of an object should not be confused with the length of its shortest side

3.

What is the area of a triangle that has a base of 37 cm and a perpendicular height of 28 cm?

518 cm^{2}

1,063 cm^{2}

1,360 cm^{2}

1,630 cm^{2}

Area of a triangle = ^{1}⁄_{2}(b x h)

4.

If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its perimeter?

44 cm

28 cm

36 cm

It is impossible to say

Did you get it wrong by confusing the perpendicular height with the length of its shortest side? The perpendicular height is NOT the same as the length of the shortest side!

5.

Archie says that the area of a rhombus of side length 12 cm is the same as that of a square of side 12 cm. Is he right?

Always

Never

Sometimes - it depends on the size of the internal angles

Only if the perimeter is equal to 48cm

If the rhombus has a right angle, it is also a square

6.

If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its area?

49 cm^{2}

121 cm^{2}

77 cm^{2}

It is impossible to say

The formula for calculating the area of a parallelogram is A = bh (Area = base x height)

7.

Is a square also a rectangle?

Yes

No

It depends on the length of its sides

It depends on its surface area

A square is a special rectangle - its length and width are the same

8.

The two parallel sides of a trapezium have lengths 10 cm and 20 cm, and the distance between them is 15 cm. What is the area of this trapezium?

150 cm^{2}

200 cm^{2}

225 cm^{2}

250 cm^{2}

Area of a trapezium = ^{1}⁄_{2} (a + b)h

9.

If a rhombus has a base of 1.2 meters and a perpendicular height of 0.8 meters, what is its area?

0.64 m^{2}

0.80 m^{2}

0.96 m^{2}

1.44 m^{2}

Area of a rhombus = perpendicular height x side length

10.

If the area of a triangle is 420 cm^{2} and its perpendicular height is 30 cm, what is the length of its base?

24 cm

26 cm

28 cm

32 cm

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