Area practice questions

Area questions

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1. 1AreaFoundation

   What is the area of a rectangle with length 8 and width 5?What is the area of a rectangle with length 8 and width 5?

   • A4040
   • B2626
   • C8080
   • D1313
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   Answer: 4040

   Area of a rectangle is length times width: 8 × 5 = 40. The perimeter of the same rectangle is 2(8) + 2(5) = 26, so read which one the question asked for.Area of a rectangle is length times width: 8 × 5 = 40. The perimeter of the same rectangle is 2(8) + 2(5) = 26, so read which one the question asked for.

   How did you do?Got itMissed it
2. 2AreaFoundation

   A square has perimeter 36. What is its area?A square has perimeter 36. What is its area?

   • A3636
   • B1818
   • C7272
   • D8181
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   Answer: 8181

   Work back to the side first: a perimeter of 36 means each side is 364 = 9, so the area is 9² = 81. Two steps, and the first is the one that gets skipped.Work back to the side first: a perimeter of 36 means each side is 36/4 = 9, so the area is 9^2 = 81. Two steps, and the first is the one that gets skipped.

   How did you do?Got itMissed it
3. 3AreaFoundation

   A triangle has base 10 and height 7. What is its area?A triangle has base 10 and height 7. What is its area?

   • A17.517.5
   • B3535
   • C140140
   • D7070
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   Answer: 3535

   Triangle area is one-half times base times height: 10 × 7 = 70, and 702 = 35.Triangle area is one-half times base times height: 10 × 7 = 70, and 70/2 = 35.

   How did you do?Got itMissed it
4. 4AreaFoundation

   A rectangle has a perimeter of 34 cm and a width of 6 cm. What is its area?A rectangle has a perimeter of 34 cm and a width of 6 cm. What is its area?

   • A66 square cm66 square cm
   • B204 square cm204 square cm
   • C28 square cm28 square cm
   • D102 square cm102 square cm
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   Answer: 66 square cm66 square cm

   The perimeter is 2(length + width), so 2(length + 6) = 34 gives length = 11 cm. The area is then 11 × 6 = 66 square cm. Multiplying the perimeter by the width gives 204.The perimeter is 2(length + width), so 2(length + 6) = 34 gives length = 11 cm. The area is then 11 × 6 = 66 square cm. Multiplying the perimeter by the width gives 204.

   How did you do?Got itMissed it
5. 5AreaStandard

   A trapezoid has bases of length 6 and 10 and height 4. What is its area?A trapezoid has bases of length 6 and 10 and height 4. What is its area?

   • A6464
   • B1616
   • C2424
   • D3232
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   Answer: 3232

   Area = one-half times the sum of the bases times the height: 6 + 102 = 8, and 8 × 4 = 32.Area = one-half times the sum of the bases times the height: (6 + 10)/2 = 8, and 8 × 4 = 32.

   How did you do?Got itMissed it
6. 6AreaStandard

   A rectangle has perimeter 34 and length 10. What is its area?A rectangle has perimeter 34 and length 10. What is its area?

   • A140140
   • B170170
   • C240240
   • D7070
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   Answer: 7070

   Perimeter 34 with length 10 gives 2(10) + 2w = 34, so w = 7. The area is 10 × 7 = 70.Perimeter 34 with length 10 gives 2(10) + 2w = 34, so w = 7. The area is 10 × 7 = 70.

   How did you do?Got itMissed it
7. 7AreaStandard

   A circle of radius 3 is cut from a square of side 6. What area remains, in terms of π?A circle of radius 3 is cut from a square of side 6. What area remains, in terms of π?

   • A36 - 6π36 - 6π
   • B36 - 3π36 - 3π
   • C36 - 9π36 - 9π
   • D18 - 9π18 - 9π
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   Answer: 36 - 9π36 - 9π

   The square has area 36 and the circle π(3)² = 9π. The circle fits exactly inside, so the remaining area is 36 - 9π.The square has area 36 and the circle π(3)^2 = 9π. The circle fits exactly inside, so the remaining area is 36 - 9π.

   How did you do?Got itMissed it
8. 8AreaStandard

   A triangle has vertices at (0, 0), (6, 0) and (0, 8). What is its area?A triangle has vertices at (0, 0), (6, 0) and (0, 8). What is its area?

   • A1010
   • B4848
   • C2424
   • D1414
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   Answer: 2424

   The legs along the axes are the base and height, 6 and 8. Area is (12)(6)(8) = 24. The value 48 is the rectangle, not the triangle.The legs along the axes are the base and height, 6 and 8. Area is (1/2)(6)(8) = 24. The value 48 is the rectangle, not the triangle.

   How did you do?Got itMissed it
9. 9AreaStandard

   A triangle has a base of 18 cm and a height of 11 cm. Enter its area in square centimeters.A triangle has a base of 18 cm and a height of 11 cm. Enter its area in square centimeters.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 9999

   The area of a triangle is half the base times the height: 18 × 112 = 1982 = 99 square cm. Forgetting to halve gives 198.The area of a triangle is half the base times the height: (18 × 11)/2 = 198/2 = 99 square cm. Forgetting to halve gives 198.

   How did you do?Got itMissed it
10. 10AreaStandard

    A parallelogram has a base of 14 cm and a perpendicular height of 9 cm. What is its area?A parallelogram has a base of 14 cm and a perpendicular height of 9 cm. What is its area?

    • A63 square cm63 square cm
    • B126 square cm126 square cm
    • C23 square cm23 square cm
    • D46 square cm46 square cm
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    Answer: 126 square cm126 square cm

    The area of a parallelogram is base times perpendicular height: 14 × 9 = 126 square cm. Halving it, as for a triangle, gives 63.The area of a parallelogram is base times perpendicular height: 14 × 9 = 126 square cm. Halving it, as for a triangle, gives 63.

    How did you do?Got itMissed it
11. 11AreaChallenge

    A trapezium has parallel sides of 14 cm and 22 cm and a height of 9 cm. What is its area?A trapezium has parallel sides of 14 cm and 22 cm and a height of 9 cm. What is its area?

    • A324 square cm324 square cm
    • B126 square cm126 square cm
    • C198 square cm198 square cm
    • D162 square cm162 square cm
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    Answer: 162 square cm162 square cm

    The area is the average of the parallel sides times the height: 14 + 222 = 18, and 18 × 9 = 162 square cm. Forgetting to halve gives 324, and using one parallel side alone gives 126 or 198.The area is the average of the parallel sides times the height: (14 + 22)/2 = 18, and 18 × 9 = 162 square cm. Forgetting to halve gives 324, and using one parallel side alone gives 126 or 198.

    How did you do?Got itMissed it
12. 12AreaChallenge

    A closed cylinder has a radius of 5 and a height of 9. What is its total surface area, in terms of π?A closed cylinder has a radius of 5 and a height of 9. What is its total surface area, in terms of π?

    • A90π90π
    • B140π140π
    • C115π115π
    • D225π225π
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    Answer: 140π140π

    The curved surface is 2π r h = 90π, and the two circular ends add 2π r² = 50π, giving 140π. Leaving out one end gives 115π and leaving out both gives 90π.The curved surface is 2π r h = 90π, and the two circular ends add 2π r^2 = 50π, giving 140π. Leaving out one end gives 115π and leaving out both gives 90π.

    How did you do?Got itMissed it