Free Geometry Worksheets With Answers
These free geometry worksheets span grades 3 to 8, covering perimeter and area, angle rules, surface area and volume, and the Pythagorean theorem, with every answer worked through. Geometry rewards students who write the formula down before substituting, so each solution shows that step explicitly. The same skills can be generated as a printable geometry test with a matching answer key.
Grades 3–8 · 9 free questions with worked answers · No sign-up to practise
Skills covered in these geometry worksheets
- Perimeter and area of rectangles and triangles
- Area and circumference of circles
- Angles on a line, around a point, and in a triangle
- Properties of 2D shapes and quadrilaterals
- Volume and surface area of prisms
- The Pythagorean theorem
Free geometry practice questions with answers
Every question below includes the final answer and the steps behind it, so the sheet doubles as its own answer key. Filter by grade or difficulty to build the set you need.
- Question 1easyGrade 3
A rectangle is 8 cm by 5 cm. What is its perimeter?
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Answer: 26 cm
Perimeter = 2(l + w) = 2(8 + 5) = 2 × 13 = 26 cm. Perimeter uses linear units.
- Question 2easyGrade 4
A rectangle is 8 cm by 5 cm. What is its area?
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Answer: 40 cm²
Area = length × width = 8 × 5 = 40. Area uses square units, so the answer is 40 cm².
- Question 3easyGrade 5
Two angles on a straight line measure 65° and x. Find x.
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Answer: 115°
Angles on a straight line sum to 180°, so x = 180 − 65 = 115°.
- Question 4mediumGrade 6
A triangle has a base of 12 cm and a height of 7 cm. What is its area?
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Answer: 42 cm²
Area = ½ × base × height = ½ × 12 × 7 = 42 cm². The ½ is the step most often skipped.
- Question 5mediumGrade 7
A circle has a radius of 5 cm. What is its area? Use π ≈ 3.14.
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Answer: 78.5 cm²
Area = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 cm². Square the radius before multiplying by π.
- Question 6mediumGrade 6
A rectangular prism measures 4 cm by 3 cm by 6 cm. What is its volume?
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Answer: 72 cm³
Volume = length × width × height = 4 × 3 × 6 = 72 cm³. Volume uses cubic units.
- Question 7hardGrade 8
A right triangle has legs of 6 cm and 8 cm. How long is the hypotenuse?
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Answer: 10 cm
By the Pythagorean theorem, c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm.
- Question 8hardGrade 8
What is the surface area of a cube with edge 5 cm?
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Answer: 150 cm²
One face has area 5² = 25 cm². A cube has six faces, so the surface area is 6 × 25 = 150 cm².
- Question 9hardGrade 7
Two angles in a triangle are 47° and 68°. Find the third angle.
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Answer: 65°
Angles in a triangle sum to 180°, so the third angle is 180 − 47 − 68 = 65°.
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Units are part of the answer
Perimeter is measured in units, area in square units, and volume in cubic units. A numerically correct answer with the wrong unit is marked wrong on almost every state assessment, and the mistake usually signals that the student applied a memorised formula without picturing the quantity. Asking which of the three a question wants, before any calculation happens, catches the error at the point where it is cheap to fix.
Write the formula before substituting
The area of a triangle is ½ × base × height and the volume of a rectangular prism is length × width × height. Students who write the formula on its own line and then substitute make far fewer errors than students who go straight to numbers, because the formula line makes a missing factor visible. This habit matters most in surface area questions, where six faces have to be accounted for.
Common mistakes to watch for
- Giving area in linear units or perimeter in square units.
- Forgetting the ½ in the triangle area formula.
- Using the diameter in place of the radius in circle formulas, which quadruples the area.
- Using a slant length instead of the perpendicular height when finding the area of a triangle.