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Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Perimeter and Area 2 (Questions)

This Math quiz is called 'Shapes - Perimeter and Area 2' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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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. 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
2. Is a square also a rectangle?
[ ] Yes
[ ] No
[ ] It depends on the length of its sides
[ ] It depends on its surface area
3. If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its area?
[ ] 49 cm2
[ ] 121 cm2
[ ] 77 cm2
[ ] It is impossible to say
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
5. What is the area of a triangle that has a base of 37 cm and a perpendicular height of 28 cm?
[ ] 518 cm2
[ ] 1,063 cm2
[ ] 1,360 cm2
[ ] 1,630 cm2
6. If the area of a triangle is 420 cm2 and its perpendicular height is 30 cm, what is the length of its base?
[ ] 24 cm
[ ] 26 cm
[ ] 28 cm
[ ] 32 cm
7. 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 cm2
[ ] 200 cm2
[ ] 225 cm2
[ ] 250 cm2
8. A garden is in the shape of a trapezium and it has an area of 1,500 meters2. 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
9. 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
10. If a rhombus has a base of 1.2 meters and a perpendicular height of 0.8 meters, what is its area?
[ ] 0.64 m2
[ ] 0.80 m2
[ ] 0.96 m2
[ ] 1.44 m2
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Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Perimeter and Area 2 (Answers)
1. In many formulas you will see the letter h which stands for 'height'. What would be a more correct term for 'height'?
[x] 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
2. Is a square also a rectangle?
[x] 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
3. If a parallelogram has a perpendicular height of 7 cm and a base of 11 cm, what is its area?
[ ] 49 cm2
[ ] 121 cm2
[x] 77 cm2
[ ] It is impossible to say
The formula for calculating the area of a parallelogram is A = bh (Area = base x height)
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
[x] 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. What is the area of a triangle that has a base of 37 cm and a perpendicular height of 28 cm?
[x] 518 cm2
[ ] 1,063 cm2
[ ] 1,360 cm2
[ ] 1,630 cm2
Area of a triangle = 1⁄2(b x h)
6. If the area of a triangle is 420 cm2 and its perpendicular height is 30 cm, what is the length of its base?
[ ] 24 cm
[ ] 26 cm
[x] 28 cm
[ ] 32 cm
7. 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 cm2
[ ] 200 cm2
[x] 225 cm2
[ ] 250 cm2
Area of a trapezium = 1⁄2 (a + b)h
8. A garden is in the shape of a trapezium and it has an area of 1,500 meters2. 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
[x] 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
9. 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
[x] 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
10. If a rhombus has a base of 1.2 meters and a perpendicular height of 0.8 meters, what is its area?
[ ] 0.64 m2
[ ] 0.80 m2
[x] 0.96 m2
[ ] 1.44 m2
Area of a rhombus = perpendicular height x side length
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