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Area and Volume Practice Tests

These Grade 10 Geometry practice tests develop measurement fluency with plane figures, surface area, volume, composite solids, scale factors, and real-world applications.

Skills covered

  • Calculating the area of rectangles, triangles, parallelograms, trapezoids, circles, rhombi, kites, and regular polygons
  • Finding surface area from faces, nets, and formulas for prisms, cylinders, pyramids, cones, spheres, and rectangular prisms
  • Finding volume of prisms, cylinders, pyramids, cones, spheres, cubes, and composite solids
  • Understanding square and cubic unit conversions and how area and volume scale
  • Applying area and volume to flooring, painting, packaging, aquariums, patios, tanks, and other practical measurements

How to use these practice tests

Sketch the figure, label the dimensions, and decide whether the problem asks for area, surface area, or volume. Keep square units for area and cubic units for volume.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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5 Tests
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1. Test

Grade 10 Area and Volume Practice Tests

Practice Grade 10 Geometry questions about plane area, surface area, volume, prisms, cylinders, pyramids, cones, spheres, scale factors, and applications.

Choose the best answer. Identify the shape, select the correct formula, substitute the measurements, and report the answer with square or cubic units.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the area of a rectangle?

Please select an answer first.

Correct answer: A

The correct answer is Length multiplied by width..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: The rectangle area formula is A=lwA=lw.
  3. Check the units: The correct answer is Length multiplied by width..

The rectangle area formula is A=lwA=lw.

2. QuestionMultiple choice

What is the area of a triangle with base b and height h?

Please select an answer first.

Correct answer: B

The correct answer is A=12bhA=\frac{1}{2}bh..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A triangle has half the area of a parallelogram with the same base and height.
  3. Check the units: The correct answer is A=12bhA=\frac{1}{2}bh..

A triangle has half the area of a parallelogram with the same base and height.

3. QuestionMultiple choice

What is the area of a parallelogram?

Please select an answer first.

Correct answer: C

The correct answer is Base multiplied by height..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: The parallelogram area formula is A=bhA=bh, using the perpendicular height.
  3. Check the units: The correct answer is Base multiplied by height..

The parallelogram area formula is A=bhA=bh, using the perpendicular height.

4. QuestionMultiple choice

What is the area of a trapezoid with bases b₁ and b₂ and height h?

Please select an answer first.

Correct answer: D

The correct answer is A=12(b1+b2)hA=\frac{1}{2}(b_1+b_2)h..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: The trapezoid area is half the sum of the bases multiplied by the height.
  3. Check the units: The correct answer is A=12(b1+b2)hA=\frac{1}{2}(b_1+b_2)h..

The trapezoid area is half the sum of the bases multiplied by the height.

5. QuestionMultiple choice

What is the area of a circle with radius r?

Please select an answer first.

Correct answer: A

The correct answer is A=πr2A=\pi r^2..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: The circle area formula is A=πr2A=\pi r^2.
  3. Check the units: The correct answer is A=πr2A=\pi r^2..

The circle area formula is A=πr2A=\pi r^2.

6. QuestionMultiple choice

A rectangle measures 9 cm by 4 cm. What is its area?

Please select an answer first.

Correct answer: B

The correct answer is 36 cm²..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: Multiply length and width: 9 · 4 = 36 square centimeters.
  3. Check the units: The correct answer is 36 cm²..

Multiply length and width: 9 · 4 = 36 square centimeters.

7. QuestionMultiple choice

What is the area of a rhombus with diagonals 10 and 14?

Please select an answer first.

Correct answer: C

The correct answer is 70 square units..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: Use A=12d1d2=12(10)(14)=70A=\frac{1}{2}d_1d_2=\frac{1}{2}(10)(14)=70.
  3. Check the units: The correct answer is 70 square units..

Use A=12d1d2=12(10)(14)=70A=\frac{1}{2}d_1d_2=\frac{1}{2}(10)(14)=70.

8. QuestionMultiple choice

What is the area of a kite with diagonals 8 and 12?

Please select an answer first.

Correct answer: D

The correct answer is 48 square units..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: The kite area is half the product of the diagonals: 12(8)(12)=48\frac{1}{2}(8)(12)=48.
  3. Check the units: The correct answer is 48 square units..

The kite area is half the product of the diagonals: 12(8)(12)=48\frac{1}{2}(8)(12)=48.

9. QuestionMultiple choice

What is the area of a regular polygon with perimeter P and apothem a?

Please select an answer first.

Correct answer: A

The correct answer is A=12PaA=\frac{1}{2}Pa..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A regular polygon can be divided into triangles, giving A=12PaA=\frac{1}{2}Pa.
  3. Check the units: The correct answer is A=12PaA=\frac{1}{2}Pa..

A regular polygon can be divided into triangles, giving A=12PaA=\frac{1}{2}Pa.

10. QuestionMultiple choice

How many square centimeters are in 2 square meters?

Please select an answer first.

Correct answer: B

The correct answer is 20,000 cm²..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: Since 1 m = 100 cm, 1 m² = 10,000 cm²; therefore 2 m² = 20,000 cm².
  3. Check the units: The correct answer is 20,000 cm²..

Since 1 m = 100 cm, 1 m² = 10,000 cm²; therefore 2 m² = 20,000 cm².

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