Area of Triangles & Quadrilaterals — Practice
Every area formula in this unit comes from a rectangle that has been cut up or rearranged.
What these questions cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Parallel — Same slope, different intercept.
- Parallelogram — A quadrilateral with both pairs of opposite sides parallel.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
- Base — Any side of a triangle, chosen as the one to measure from.
- Height — The perpendicular distance from the base to the opposite corner.
- Cubic unit — A cube one unit on every edge.
Problem 1
Find the area of a triangle with base 10 and height 6.
Worked answer
30
12 × 10 × 6 = 30
Problem 2
Find the area of a triangle with base 7 and height 4.
Worked answer
14
14
Problem 3
Find the area of a rectangle 9 by 5.
Worked answer
45
45
Problem 4
Find the area of a parallelogram with base 8 and height 5.
Worked answer
40
8 × 5 = 40
Problem 5
Find the perimeter of a rectangle 9 by 5.
Worked answer
28
2(9)+2(5) = 28
Problem 6
Find the area of a trapezoid with parallel sides 8 and 14 and height 5.
Worked answer
55
8+142 = 11
11 × 5 = 55
Problem 7
Find the area of a trapezoid with parallel sides 6 and 10 and height 4.
Worked answer
32
8 × 4 = 32
Problem 8
A triangle has base 6 and equal sides 5. Its height is 4. Find the area.
Worked answer
12
12 × 6 × 4 = 12
Problem 9
A triangle has area 24 and base 8. Find its height.
Worked answer
6
12 × 8 × h = 24
4h = 24, so h = 6
Problem 10
An L-shape is a 10 by 8 rectangle with a 4 by 3 corner removed. Find its area.
Worked answer
68
80 - 12 = 68
Problem 11
Area is measured in
- square units
- units
- cubic units
- degrees
Worked answer
square units
So the units are squared
Problem 12
A shape is a 6 by 4 rectangle with a triangle of base 6 and height 3 on top. Find the total area.
Worked answer
33
24 + 9 = 33
Problem 13
A parallelogram has area 56 and height 7. Find its base.
Worked answer
8
b = 8
Problem 14
Find the area of a triangle with base 4.5 and height 8.
Worked answer
18
12 × 4.5 × 8 = 18
Problem 15
A rectangle 12 by 5 has a 3 by 3 square cut from one corner. Find the remaining area.
Worked answer
51
60 - 9 = 51
Problem 16
A trapezoid has area 45, height 5 and one parallel side 7. Find the other.
Worked answer
11
7+b2 × 5 = 45
7+b2 = 9, so b = 11