Area — Grade 7 Accelerated, what it means and where it is taught
Space inside, measured in square units.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Surface area — Total area of all the outside faces, in square units.
- Riemann sum — An estimate of area made from rectangles under a curve.
- Definite integral — The exact area, written ∫ab f(x)dx.
Practise this idea
82 questions in the course bank use Area, in Proportional Reasoning with Scale Drawings, Length and Area in 2-D Figures, Plane Sections of 3-D Figures, Volume & Surface Area of 3-D Figures, Squares & Square Roots, Measurement. The first 8 are below; the rest are in those units.
Problem 1
A 3 × 4 rectangle is scaled by factor 2. Find the new area.
Worked answer
48
New rectangle: 6 × 8 = 48
Check: original area 12, times 22 = 4, gives 48 ✓
Problem 2
If every length is multiplied by 4, the area is multiplied by what?
- 4
- 8
- 16
- 64
Worked answer
16
k2 = 42 = 16
Problem 3
A floor plan at 1 : 40 shows a room 8.5 cm by 6 cm. Find the real area in square metres.
Worked answer
8.16
8.5 × 40 = 340 cm = 3.4 m
6 × 40 = 240 cm = 2.4 m
3.4 × 2.4 = 8.16 m2
Problem 4
A model car is 112 scale. The real hood has area 3.6 m2. Find the model hood's area in m2.
Worked answer
0.025
3.6 ÷ 144 = 0.025 m2
Problem 5
Two similar figures have areas 25 cm2 and 64 cm2. The smaller has perimeter 20 cm. Find the larger perimeter.
Worked answer
32
k2 = 6425, so k = 85
Perimeter is a length, so it scales by k
20 × 85 = 32 cm
Problem 6
Find the area of a rectangle 7 cm by 9 cm.
Worked answer
63
7 × 9 = 63 cm2
Problem 7
Find the area of a triangle with base 10 and height 6.
Worked answer
30
12(10)(6) = 30
Problem 8
Find the area of a parallelogram with base 12 and height 5.
Worked answer
60
12 × 5 = 60