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.
Alaska 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
Perimeter & Area in Alaska
In the Alaska content 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.
Source: Alaska Department of Education and Early Development
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 triangle has a base of 18 cm and a height of 8 cm. What is its area?
answer boxcm²
72 cm²
Hint: A triangle is half of a parallelogram with the same base and height, so area = base × height ÷ 2.
Question 2
A trapezoid has parallel sides of 10 cm and 14 cm, and a height of 9 cm. What is its area?
answer boxcm²
108 cm²
Hint: Add the parallel sides, multiply by the height, then divide by 2: (a + b) × h ÷ 2.
Question 3
Two triangles have the same base and the same height but look different. What is true about their areas?
- You need the perimeter to tell
- Their areas are equal
- The one that leans more has less area
- The one with longer sides has more area
Their areas are equal
Hint: The area of a triangle only depends on its base and height: base × height ÷ 2.
Question 4
A parking space is painted as a parallelogram with a base of 9 m, a height of 3 m and slanted sides of 6 m. What is its area?
- 13.5 m²
- 30 m²
- 54 m²
- 27 m²
27 m²
Hint: Area of a parallelogram = base × perpendicular height. The slanted side is only needed for perimeter.
Question 5
A parallelogram has a base of 14 m, slanted sides of 4 m, and a height of 3 m. What is its area?
answer boxm²
42 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 12 m, 9 m, 4 m and 9 m. How long is the last side?
answer boxm
11 m
Hint: Add the sides you know. The missing side is the perimeter minus that total.