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.
Alabama Course of Study content standard: 6.26 · area of triangles, special 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
Perimeter & Area in Alabama
In the Alabama Course of Study, this is unit 7 of 17 in 6th grade Math, after Equations and before Volume & Capacity.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
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 triangular sail has a base of 6 m and a height of 7 m. How much fabric covers the sail?
- 26 m²
- 42 m²
- 21 m²
- 13 m²
21 m²
Hint: Fabric covering a surface is an area question. Area of a triangle = base × height ÷ 2.
Question 3
Why does the triangle area formula divide by 2?
- Because a triangle has 3 sides
- To change centimeters into meters
- A triangle is half of a parallelogram with the same base and height
- Because the height is always half the base
A triangle is half of a parallelogram with the same base and height
Hint: Copy the triangle, turn the copy around and join them. Together they make a parallelogram.
Question 4
A triangle has a base of 10 cm and a height of 7 cm. What is its area?
answer boxcm²
35 cm²
Hint: A triangle is half of a parallelogram with the same base and height, so area = base × height ÷ 2.
Question 5
A trapezoid has parallel sides of 5 cm and 14 cm, and a height of 10 cm. What is its area?
answer boxcm²
95 cm²
Hint: Add the parallel sides, multiply by the height, then divide by 2: (a + b) × h ÷ 2.
Question 6
A parallelogram has a base of 6 m, slanted sides of 6 m, and a height of 4 m. What is its area?
answer boxm²
24 m²
Hint: Area of a parallelogram = base × perpendicular height. The slanted side is not the height.