6th grade · Math · Unit 7 of 17
Perimeter & Area
Triangles, parallelograms, trapezoids
What your child practices
Finding the perimeter of L-shapes and other polygons, and the area of triangles (b × h ÷ 2), parallelograms (b × h) and trapezoids ((a + b) × h ÷ 2), including working backwards to a missing measurement.
California Content Standards learning standard: 6.G.1 · area of triangles, quadrilaterals and other polygons
How we explain it
Children can open this short lesson before they practice.
- Perimeter is the distance around. Add every side.
- Triangle area = base × height ÷ 2.
- Parallelogram area = base × height. Trapezoid area = (a + b) × height ÷ 2.
Example: A triangle has a base of 8 cm and a height of 5 cm. What is its area? 8 × 5 = 40. 40 ÷ 2 = 20. Answer: 20 cm²
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Join the points in order, A to F, then back to A. Each grid square is 1 m long. What is the perimeter of the shape?
answer boxm
24 m
Hint: Add all 6 sides. Shortcut: the two short steps add up to the full width and height, so the perimeter equals the perimeter of the rectangle around the shape.
Question 2
A trapezoid has parallel sides of 3 cm and 7 cm, and a height of 2 cm. What is its area?
answer boxcm²
10 cm²
Hint: Add the parallel sides, multiply by the height, then divide by 2: (a + b) × h ÷ 2.
Question 3
A parallelogram has an area of 36 cm² and a base of 9 cm. What is its height?
answer boxcm
4 cm
Hint: Area = base × height, so height = area ÷ base.
Question 4
A triangular sail has a base of 2 m and a height of 5 m. How much fabric covers the sail?
- 5 m²
- 10 m²
- 7 m²
- 14 m²
5 m²
Hint: Fabric covering a surface is an area question. Area of a triangle = base × height ÷ 2.
Question 5
A garden shaped like a pentagon has a perimeter of 55 m. 4 of its sides are 12 m, 12 m, 10 m and 14 m. How long is the last side?
answer boxm
7 m
Hint: Add the sides you know. The missing side is the perimeter minus that total.
Question 6
A parallelogram has a base of 13 m, slanted sides of 12 m, and a height of 10 m. What is its area?
answer boxm²
130 m²
Hint: Area of a parallelogram = base × perpendicular height. The slanted side is not the height.