Area of triangles and parallelograms: what children learn
In this game children work out the area of four shapes and put them in order from smallest to largest. Each round mixes triangles and parallelograms, so children need to remember which formula halves and which does not.
Supports part of Common Core 6.G.A.1: area of triangles and parallelograms. This focused game does not cover the entire standard.
Common Core connection: 6.G.A.1. This is focused practice for part of the standard.
How to play
Put the numbers in order. Use the arrow buttons, or pick one card and then another to swap them. Each game has 5 rounds. After you press Check, the correct order is shown if you got it wrong.
Step by step
- Parallelogram: base × height. Cut a triangle off one end of a parallelogram and move it to the other end, and you get a rectangle. So the area is base × height.
- Triangle: half of base × height. Two identical triangles make a parallelogram, so a triangle's area is ½ × base × height.
- Use the perpendicular height. The height is measured at right angles to the base, not along the sloping side.
- Compare and order. Work out each area in cm², then put them in order from smallest to largest.
Worked examples
Example 1: What is the area of a triangle with base 6 cm and height 4 cm?
Working: 6 × 4 = 24, and half of 24 is 12.
Answer: 12 cm²
Example 2: What is the area of a parallelogram with base 5 cm and height 3 cm?
Working: 5 × 3 = 15.
Answer: 15 cm²
Example 3: Which is bigger: a triangle with base 10 cm and height 5 cm, or a parallelogram with base 4 cm and height 4 cm?
Working: Triangle: 10 × 5 ÷ 2 = 25. Parallelogram: 4 × 4 = 16.
Answer: The triangle, 25 cm²
Common mistakes and how to fix them
- Forgetting to halve for a triangle. Draw the matching triangle to make a parallelogram. The triangle is half of it.
- Halving for a parallelogram too. Only triangles are halved. A parallelogram is the same area as a rectangle with the same base and height.
- Using the slanted side as the height. The height is the straight-up distance, at a right angle to the base.
Activities to try at home
- Cut a parallelogram out of paper and rearrange it into a rectangle.
- Cut a rectangle along its diagonal to show that each triangle is half.
- Spot triangles and parallelograms in buildings, roofs and patterns.
Ideas for the classroom
- Students draw triangles with the same base and height but different shapes, and show they have the same area.
- Find the area of shapes on squared paper, then check with the formula.
- Investigate: if you double the base of a triangle, what happens to the area?
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
How should I choose this game for my learner?
Supports part of Common Core 6.G.A.1: area of triangles and parallelograms. This focused game does not cover the entire standard.
Why does the height have to be perpendicular?
The formula comes from rearranging the shape into a rectangle, whose height is straight up from the base.
Does every triangle use the same formula?
Yes. Right-angled, isosceles, equilateral and scalene triangles all have area ½ × base × height.
Can it be played with a keyboard?
Yes. Tab to a card's up or down arrow button and press Enter or Space to move it, then choose Check.