Length and Area in 2-D Figures — Drills
Length and Area in 2-D Figures has 8 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 13 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.
- Circumference — The perimeter of a circle: C = 2π r.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Base — The number being multiplied. In 53 the base is 5.
- Radius — Centre to edge. Half the diameter.
- Diameter — All the way across through the centre. d = 2r.
- Parallel — Same slope, different intercept.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Parallelogram — A quadrilateral with both pairs of opposite sides parallel.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
- Height — The perpendicular distance from the base to the opposite corner.
Rectangle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the area of a rectangle 6 cm by 11 cm.
Worked answer
66
6 × 11 = 66 cm2
Problem 2
Find the area of a rectangle 10 cm by 9 cm.
Worked answer
90
10 × 9 = 90 cm2
Triangle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the area of a triangle with base 14 and height 10.
Worked answer
70
12(14)(10) = 70
Problem 2
Find the area of a triangle with base 20 and height 8.
Worked answer
80
12(20)(8) = 80
Trapezoid
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A trapezoid has parallel sides 4 and 10, and height 9. Find its area.
Worked answer
63
4 + 102 = 7
7 × 9 = 63
Problem 2
A trapezoid has parallel sides 7 and 12, and height 4. Find its area.
Worked answer
38
7 + 122 = 9.5
9.5 × 4 = 38
Circle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the circumference of a circle with radius 4. Use π ≈ 3.14.
Worked answer
25.12
2 × 3.14 × 4 = 25.12
Problem 2
Find the area of a circle with radius 6. Use π ≈ 3.14.
Worked answer
113.04
62 = 36
3.14 × 36 = 113.04
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A triangle has area 27 and base 6. Find its height.
Worked answer
9
27 = 12(6)h = 3h
h = 27 ÷ 3 = 9
Problem 2
A triangle has area 42 and base 12. Find its height.
Worked answer
7
42 = 12(12)h = 6h
h = 42 ÷ 6 = 7
Perimeter
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A rectangle has perimeter 36 and length 7. Find its width.
Worked answer
11
14 + 2w = 36
2w = 22
w = 11
Problem 2
A rectangle has perimeter 38 and length 11. Find its width.
Worked answer
8
22 + 2w = 38
2w = 16
w = 8
Parallelogram
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A parallelogram has base 14 and perpendicular height 7. Its slanted side measures 9. Find its area.
Worked answer
98
14 × 7 = 98
The 9 is a distractor — the formula wants the perpendicular height.
Problem 2
A parallelogram has base 4 and perpendicular height 5. Its slanted side measures 10. Find its area.
Worked answer
20
4 × 5 = 20
The 10 is a distractor — the formula wants the perpendicular height.
Composite figures
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A 9 × 9 rectangle has a 5 × 7 rectangle cut from one corner. Find the remaining area.
Worked answer
46
9 × 9 = 81
5 × 7 = 35
81 - 35 = 46
Problem 2
A 11 × 7 rectangle has a 2 × 4 rectangle cut from one corner. Find the remaining area.
Worked answer
69
11 × 7 = 77
2 × 4 = 8
77 - 8 = 69