Question

a scale drawing for a backyard is shown below.
in the drawing, 2 cm represents 3 m.
assuming the patio is rectangular, find the area of the real patio.
image of a backyard scale drawing with lawn and patio, patio has dimensions 6 cm (length) and 4 cm (width) in the drawing
area of the real patio: m²

Explanation:

Step1: Find scale factor (cm to m)

Scale: $2\ \text{cm} = 3\ \text{m}$, so $1\ \text{cm} = \frac{3}{2}\ \text{m} = 1.5\ \text{m}$

Step2: Convert patio length to real length

Drawing length: $6\ \text{cm}$
Real length: $6 \times 1.5 = 9\ \text{m}$

Step3: Convert patio width to real width

Drawing width: $4\ \text{cm}$
Real width: $4 \times 1.5 = 6\ \text{m}$

Step4: Calculate real patio area

Area = length $\times$ width

Answer:

$9 \times 6 = 54$
The area of the real patio is $\boldsymbol{54}\ \text{m}^2$