What is the formula for the area of a rectangle?

The area of a rectangle is calculated by multiplying its length by its width (Area = L × W).

How do you calculate the area of a triangle?

The area of a triangle is half the product of its base and its height (Area = 1/2 × B × H).

The area of a trapezoid is half its height multiplied by the sum of its two parallel bases: Area = 1/2 × H × (B1 + B2).

The formulas to calculate the areas of common 2D shapes are presented below:

Rectangle

Area = L × W

Square

Area = S²

Triangle

Area = ½ × H × B

Parallelogram

Area = L × H

Trapezoid

Area = ½ × H × (B₁ + B₂)

Use the grid to determine the dimensions of the figures below and then use the formulas to calculate their areas.

View Solution

We first determine the dimensions needed to calculate the area from the grid, then use the appropriate formulas for each figure.

a) The figure is a rectangle of width \(AD = 3\) units and length \(DC = 4\) units.
\(\text{Area} = \text{Length} \times \text{Width} = 4 \times 3 = 12 \text{ units}^2\)
b) The figure is a square of side \(HG = 3\) units.
\(\text{Area} = \text{Side} \times \text{Side} = 3 \times 3 = 9 \text{ units}^2\)
c) The figure is a right triangle of height \(H = ML = 3\) units and base \(B = MN = 4\) units.
\(\text{Area} = \frac{1}{2} \times H \times B = \frac{1}{2} \times 3 \times 4 = 6 \text{ units}^2\)
d) The figure is a right triangle with the same dimensions as part c): Height \(H = IJ = 3\) units and base \(B = JK = 4\) units.
\(\text{Area} = \frac{1}{2} \times H \times B = \frac{1}{2} \times 3 \times 4 = 6 \text{ units}^2\)
e) The figure is a parallelogram of length \(L = OP = 5\) units and the perpendicular height \(H\) between \(OP\) and \(RQ\) is \(3\) units.

\(\text{Area} = L \times H = 5 \times 3 = 15 \text{ units}^2\)
Note that H is perpendicular to both OP and RQ.

Determine the dimensions of the figures below from the grid and then calculate their areas.

View Solution

We first identify the figure, determine its dimensions from the grid, and then calculate the area.

a) The figure is a trapezoid with \(AB\) and \(DC\) parallel. Base \(B_1 = DC = 2\) units, base \(B_2 = AB = 4\) units, and the height \(H = AD = 3\) units.
\(\text{Area} = \frac{1}{2} \times H \times (B_1 + B_2) = \frac{1}{2} \times 3 \times (2 + 4) = \frac{1}{2} \times 3 \times 6 = 9 \text{ units}^2\)
b) The figure is a trapezoid with \(GF\) and \(HE\) parallel. Base \(B_1 = GF = 2\) units, base \(B_2 = HE = 4\) units, and the height \(H = 2\) units.
\(\text{Area} = \frac{1}{2} \times H \times (B_1 + B_2) = \frac{1}{2} \times 2 \times (2 + 4) = \frac{1}{2} \times 2 \times 6 = 6 \text{ units}^2\)
c) The figure is a triangle of base \(B = LN = 5\) units and height \(H = 4\) units.

\(\text{Area} = \frac{1}{2} \times B \times H = \frac{1}{2} \times 5 \times 4 = \frac{20}{2} = 10 \text{ units}^2\)
d) The figure is a triangle of base \(B = IK = 4\) units and height \(H = 4\) units.

\(\text{Area} = \frac{1}{2} \times B \times H = \frac{1}{2} \times 4 \times 4 = \frac{16}{2} = 8 \text{ units}^2\)
e) The figure is a trapezoid with base \(B_1 = OP = 2\) units, base \(B_2 = RQ = 7\) units, and height \(H = 3\) units.
\(\text{Area} = \frac{1}{2} \times H \times (B_1 + B_2) = \frac{1}{2} \times 3 \times (2 + 7) = \frac{1}{2} \times 3 \times 9 = 13.5 \text{ units}^2\)