Maths Quiz - Perimeter and Area (Medium) (Answers)
Perimeter and area when dealing with circular objects usually involves circumference. This is the second 11-plus Maths quiz on perimeter and area. In this quiz we are going to have a look at a few different shapes.
The following symbols may be of use in doing this quiz:
If you haven't played our easier quizzes yet, give them a go before tackling this one. Remember, take your time, read everything carefully and see if you can get top marks. Enjoy yourself!
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A regular nonagon has ALL its sides the same length ? perimeter = 9 × 8 = 72 cm
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Circumference, C = 2?r = 2 × 22?7 × 7 = 44 cm
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Area = length × width ? 150 = 50 × 3. Make sure that you USE the UNITS RIGHT!
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A cube has six faces: each face is a square. In this case, each square has a side length of 10 mm, so the area = 10 × 10 = 100 mm2. Each square makes up the face of the cube, so surface area of a cube = 6 × 100 mm2 = 600 mm2
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Suppose we have a square of side length 4 cm. Fold it in half along an axis of symmetry parallel to one of its sides: one side is now 4 cm and the other is 2 cm ? area = 2 × 4 = 8 cm2 = half of the original area of 16 cm2. Now fold it in half along an axis of symmetry parallel to the 4 cm side: one side is now 4 cm and the other is 1 cm ? area = 1 × 4 = 4 cm2 = a quarter of the original area of 16 cm2. The same is true if you fold it in half along an axis of symmetry parallel to the 2 cm side: try it!
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The area of square = 72 × 72 = 5,184 cm2. Area of the triangle = 1?2 × base × height = 1?2 × 6 × 6 = 18 cm2. The number of triangles = 5,184 ÷ 18 = 288. You have to divide 5,184 by 18 because you want to find out how many 'lots' of 18 there are in 5,184: each 'lot' equals one triangle: this is the same as adding 'lots' of 18 to itself until you get to 5,184. Incidentally, the triangles will fit because 72 is a multiple of 6: 12 × 6 = 72. There is another way of doing this problem: think about squares!
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The number of tiles = 25 ÷ 0.25 = 100. You have to divide 25 by 0.25 because you want to find out how many 'lots' of 0.25 there are in 25: each 'lot' equals one tile: this is the same as adding 'lots' of 0.25 to itself until you get to 25. By the way, 0.25 =1?4. To divide by a fraction, invert and multiply: 4 × 25 = 100
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If the circle is cut in half, the length of the perimeter of one of the half circles = the perimeter of the semi-circle + the length of the diameter of the circle = 22 + 14 = 36 cm
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The circumference, C = 2?r. If you double the radius r, then it becomes 2r. Now C = 4?r = twice the original circumference. If you have difficulty in seeing this, try this example, if r = 7 cm, C = 44 cm. If r = 14 cm, C = 88 cm. Use ? = 22?7
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The area, A = ?r2. if r = 7 cm, A = 22?7 × 7 × 7 = 154 cm. Now, if r = 14, A = 22?7 × 14 × 14 = 616 cm2 = 4 times the original area. Although a specific example is not a proof, it can be shown that this will always happen: if you double the radius, the area will quadruple
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