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.
Maine Learning Results learning standard: 6.G.A.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
Perimeter & Area in Maine
In the Maine Learning Results, 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.
Source: Maine Department of Education
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 triangle and a parallelogram have the same base and the same height. How do their areas compare?
- The triangle's area is double
- Their areas are equal
- The triangle's area is half the parallelogram's
- The triangle's area is one quarter
The triangle's area is half the parallelogram's
Hint: Two copies of the triangle fit together to make a parallelogram with the same base and height.
Question 3
A triangular sail has a base of 3 m and a height of 8 m. How much fabric covers the sail?
- 48 m²
- 22 m²
- 24 m²
- 12 m²
12 m²
Hint: Fabric covering a surface is an area question. Area of a triangle = base × height ÷ 2.
Question 4
A triangle has a base of 17 cm and a height of 4 cm. What is its area?
answer boxcm²
34 cm²
Hint: A triangle is half of a parallelogram with the same base and height, so area = base × height ÷ 2.
Question 5
A parallelogram has a base of 11 m, slanted sides of 6 m, and a height of 3 m. What is its area?
answer boxm²
33 m²
Hint: Area of a parallelogram = base × perpendicular height. The slanted side is not the height.
Question 6
A garden shaped like a pentagon has a perimeter of 45 m. 4 of its sides are 14 m, 6 m, 7 m and 12 m. How long is the last side?
answer boxm
6 m
Hint: Add the sides you know. The missing side is the perimeter minus that total.