Problem 1
A rectangle is 13 cm long and 10 cm wide. What is its perimeter?
Answer: 46 cm
- Perimeter means distance around the outside.
- Add length and width: 13 + 10 = 23.
- Double that total: 46.
How to explain it: Children often jump straight to multiplying the two dimensions. Remind them that perimeter and area are different ideas.
Problem 2
A square has side length 11 cm. What is its perimeter?
Answer: 44 cm
- All 4 sides of a square are equal.
- Multiply one side by 4: 4 × 11 = 44.
- So the perimeter is 44 cm.
How to explain it: Square questions are a good place to reinforce that one property of a shape can make the calculation faster.
Problem 3
A shape has 4 equal sides and 4 right angles. Is it always a square?
Answer: Yes
- 4 equal sides is a square property.
- 4 right angles is also a square property.
- A shape with both of those properties is a square.
How to explain it: Geometry becomes easier when children connect names to properties instead of relying only on what a picture looks like.
Problem 4
A rectangle is 12 units long and 9 units wide. How many square units cover it?
Answer: 108 square units
- Area measures the number of square units that cover a shape.
- Multiply length by width: 12 × 9 = 108.
- So the area is 108 square units.
How to explain it: If perimeter and area are getting mixed up, draw tiles inside the shape for area and trace around it for perimeter.
Problem 5
Which has the larger perimeter: a square with side 10 cm or a rectangle with length 12 cm and width 8 cm?
Answer: They have the same perimeter
- Square perimeter: 4 × 10 = 40.
- Rectangle perimeter: 2 × (12 + 8) = 40.
- Compare the two values.
How to explain it: Comparison geometry questions are easier when children calculate each shape fully before trying to compare them.
Problem 6
A triangle has side lengths 9 cm, 10 cm, and 11 cm. What is its perimeter?
Answer: 30 cm
- Perimeter of a triangle is the sum of all 3 sides.
- 9 + 10 + 11 = 30.
- So the perimeter is 30 cm.
How to explain it: Triangles help children remember that perimeter means add every outside edge, no matter the shape.
Problem 7
A shape has 1 pair of parallel sides and exactly 4 sides. Which family of shapes could it belong to?
Answer: A trapezium or trapezoid family
- The shape has 4 sides, so it is a quadrilateral.
- It has one pair of parallel sides.
- That matches the trapezium or trapezoid family.
How to explain it: Property-based geometry language is more useful than picture-matching when shapes are rotated or stretched.
Problem 8
A rectangle has area 36 square units and width 4 units. What is the length?
Answer: 9 units
- Area = length × width.
- We know the area is 36 and the width is 4.
- Divide to find length: 36 ÷ 4 = 9.
How to explain it: Reverse geometry questions are excellent for showing that formulas can be used backward too.
Problem 9
A shape has 4 sides. Two sides are long, two sides are short, and all angles are right angles. Name the shape.
Answer: Rectangle
- 4 sides with opposite sides equal suggests a quadrilateral with matching pairs.
- All angles are right angles.
- That makes the shape a rectangle.
How to explain it: When children see shape clues in words, teach them to sort by sides first, then angles.
Problem 10
A square and a rectangle both have area 60 square units. Does that mean they must have the same perimeter?
Answer: No
- Shapes can have the same area with different side lengths.
- Different side lengths can create different perimeters.
- So equal area does not force equal perimeter.
How to explain it: This is one of the best ideas for helping parents and children separate area from perimeter in a lasting way.