Answer
area of deck = $80$ $m^2$
Work Step by Step
If we want to find the area of the deck in the real world and not according to the scale drawing, let us convert the scale drawing to real world measurements first.
We know that the scale is $1$ $in.$ = $2$ $m$, so let's set up the proportion to find what the dimensions are in real life.
Let's convert the width of the pool first:
$\frac{1}{2} = \frac{2}{x}$
Use the cross products property to eliminate the fractions:
$x = 4$
Now, we convert the length of the pool:
$\frac{1}{2} = \frac{6}{x}$
Use the cross products property to eliminate the fractions:
$x = 12$ m
Next, we convert the width of the deck and pool combined:
$\frac{1}{2} = \frac{4}{x}$
Use the cross products property to eliminate the fractions:
$x = 8$ m
Finally, we convert the length of the deck and pool combined:
$\frac{1}{2} = \frac{8}{x}$
Use the cross products property to eliminate the fractions:
$x = 16$ m
We want to find the area of just the deck, which we can do if we subtract the area of the pool from the area of both the pool and the deck together.
Let's find the area of the pool by using the following formula for the area of a rectangle:
$A = lw$, where $A$ is the area, $l$ is the length, and $w$ is the width of the rectangle.
Let's substitute what we know into this formula to find the area of the pool itself:
$A = (4 m)(12 m)$
Multiply to solve:
$A = 48$ $m^2$
Now, let's find the area of the combined pool and deck:
$A = (8 m)(16 m)$
Multiply to solve:
$A = 128$ $m^2$
To find the area of the deck as depicted in the scale drawing, we subtract the area of the pool from the combined area of the pool and the deck together:
area of deck = $128$ $m^2 - 48$ $m^2$
Subtract to solve:
area of deck = $80$ $m^2$
