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.
Minnesota K-12 Academic Standards benchmark: 6.2.3.5 · the area of 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 Minnesota
In the Minnesota K-12 Academic Standards, 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
A trapezoid has parallel sides of 9 cm and 15 cm, and a height of 6 cm. What is its area?
answer boxcm²
72 cm²
Hint: Add the parallel sides, multiply by the height, then divide by 2: (a + b) × h ÷ 2.
Question 2
A triangle has a base of 10 cm and a height of 6 cm. What is its area?
answer boxcm²
30 cm²
Hint: A triangle is half of a parallelogram with the same base and height, so area = base × height ÷ 2.
Question 3
A parallelogram has an area of 32 cm² and a base of 8 cm. What is its height?
answer boxcm
4 cm
Hint: Area = base × height, so height = area ÷ base.
Question 4
A garden shaped like a pentagon has a perimeter of 62 m. 4 of its sides are 14 m, 12 m, 8 m and 14 m. How long is the last side?
answer boxm
14 m
Hint: Add the sides you know. The missing side is the perimeter minus that total.
Question 5
A triangular sail has a base of 8 m and a height of 5 m. How much fabric covers the sail?
- 80 m²
- 40 m²
- 20 m²
- 26 m²
20 m²
Hint: Fabric covering a surface is an area question. Area of a triangle = base × height ÷ 2.
Question 6
A parallelogram has a base of 7 m, slanted sides of 14 m, and a height of 11 m. What is its area?
answer boxm²
77 m²
Hint: Area of a parallelogram = base × perpendicular height. The slanted side is not the height.