Geometry

Area and perimeter

Area tasks test formulas and unit conversion. Many mistakes come from units, not from the formula.

München Named for the T-Kurs maths test at Studienkolleg München. Source

The rules

• Rectangle A = a · b; triangle A = ½ · g · h; parallelogram A = g · h; trapezoid A = ½(a + c) · h.
• Circle: A = πr², circumference U = 2πr.
• Area units step by 100: 1 m² = 100 dm² = 10 000 cm²; 1 ha = 10 000 m²; 1 km² = 100 ha.
• Composite shapes: split into simple shapes and add or subtract.

Practice questions with solutions

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. 1. A triangle has base 6 and height 9. What is its area?

   • a27
   • b15
   • c33
   • d54
   Show solution

   Answer: 27

   Area of a triangle = (base · height) / 2.

   (6 · 9) / 2 = 54 / 2 = 27.

2. 2. A triangle has base 8 and height 3. What is its area?

   • a11
   • b20
   • c12
   • d24
   Show solution

   Answer: 12

   Area of a triangle = (base · height) / 2.

   (8 · 3) / 2 = 24 / 2 = 12.

3. 3. A rectangle is 4 wide and 9 tall. What is its area?

   • a13
   • b36
   • c40
   • d26
   Show solution

   Answer: 36

   Area of a rectangle = width · height.

   4 · 9 = 36.

4. 4. A triangle has base 12 and height 5. What is its area?

   • a42
   • b30
   • c60
   • d17
   Show solution

   Answer: 30

   Area of a triangle = (base · height) / 2.

   (12 · 5) / 2 = 60 / 2 = 30.

5. 5. A rectangle is 4 wide and 7 tall. What is its area?

   • a22
   • b32
   • c11
   • d28
   Show solution

   Answer: 28

   Area of a rectangle = width · height.

   4 · 7 = 28.

6. 6. A triangle has base 4 and height 3. What is its area?

   • a7
   • b6
   • c12
   • d10
   Show solution

   Answer: 6

   Area of a triangle = (base · height) / 2.

   (4 · 3) / 2 = 12 / 2 = 6.

Common mistakes

• Converting area units by 10 instead of 100.
• Using a slanted side instead of the height.
• Mixing up radius and diameter.

Related topics

All maths topics · T-Kurs · M-Kurs · W-Kurs