6th grade · Math · Unit 7 of 21
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.
New York State Learning Standards learning standard: NY-6.G.1 · area of triangles, trapezoids 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 New York
In the New York State Learning Standards, this is unit 7 of 21 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 triangle has a base of 15 cm and a height of 14 cm. What is its area?
answer boxcm²
105 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 16 cm, and a height of 12 cm. What is its area?
answer boxcm²
156 cm²
Hint: Add the parallel sides, multiply by the height, then divide by 2: (a + b) × h ÷ 2.
Question 3
To find the area of a parallelogram, which two measurements do you multiply?
- The base and the perpendicular height
- The perimeter and the base
- The base and the slanted side
- The two slanted sides
The base and the perpendicular height
Hint: Cut a triangle off one end and slide it to the other end. You get a rectangle with the same base and height.
Question 4
A parallelogram has an area of 12 cm² and a base of 6 cm. What is its height?
answer boxcm
2 cm
Hint: Area = base × height, so height = area ÷ base.
Question 5
A parallelogram has a base of 13 m, slanted sides of 15 m, and a height of 11 m. What is its area?
answer boxm²
143 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 48 m. 4 of its sides are 15 m, 14 m, 7 m and 6 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.