# Given two rectangles: 15m by 7m and 27m by 3m. Find the combined area.

Question
Analytic geometry
Given two rectangles: 15m by 7m and 27m by 3m. Find the combined area.

2021-03-03
$$\displaystyle{\underset{{{1}+{2}}}{{{A}}}}={\underset{{{1}}}{{{A}}}}+{\underset{{{2}}}{{{A}}}}$$
A=ab
Where a and b are the sides of the rectangle:
Substitute A=ab:
$$\displaystyle{\underset{{{1}+{2}}}{{{A}}}}={\underset{{{1}}}{{{a}}}}\times{\underset{{{1}}}{{{b}}}}+{\underset{{{2}}}{{{a}}}}\times{\underset{{{2}}}{{{b}}}}$$
Substitute the given:
$$\displaystyle{\underset{{{1}+{2}}}{{{A}}}}={15}\times{7}+{27}\times{3}$$
$$\displaystyle{\underset{{{1}+{2}}}{{{A}}}}={105}+{81}$$
$$\displaystyle{\underset{{{1}+{2}}}{{{A}}}}={186}{m}^{{2}}$$

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