Two rectangles overlap with their common region being a smaller rectangle, as shown. The total area of the shaded region is
(A) 45
(D) 79
(B) 70
(E) 73
(C) 52

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-133.jpg?height=336&width=553&top_left_y=1155&top_left_x=1271)
Two rectangles overlap with their common region being a smaller rectangle, as shown. The total area of the shaded region is
(A) 45
(D) 76
(B) 70
(C) 52
(E) 73

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-259.jpg?height=358&width=610&top_left_y=282&top_left_x=1321)

Solution 1

Area (1) $=8 \times 5$ - Area (2) $=40-3=37$

Area (3) $=4 \times 9$ - Area (2) $=36-3=33$

Therefore, the shaded area equals,

$$
\text { (1) }+ \text { (2) }+ \text { (3) }=37+3+33=73 \text {. }
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-259.jpg?height=363&width=613&top_left_y=751&top_left_x=1317)

## Solution 2

Shaded area $=($ Area of $5 \times 8$ rectangle $)+($ Area of $4 \times 9$ rectangle $)-$ Overlap

$$
\begin{aligned}
& =40+36-3 \\
& =73
\end{aligned}
$$

ANSWER: (E)