In the diagram, what is the area of quadrilateral $A B C D$ ?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 28

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-124.jpg?height=255&width=366&top_left_y=957&top_left_x=1324)
If we join $A$ to $C$, then the quadrilateral is divided into two right-angled triangles.

The area of triangle $A B C$ is $\frac{1}{2}(4)(7)=14$.

To find the area of triangle $A D C$, first we need to determine the length of $A D$.

Using Pythagoras in both triangles,

$$
\begin{aligned}
A D^{2} & =A C^{2}-D C^{2} \\
A D^{2} & =\left(A B^{2}+B C^{2}\right)-1^{2} \\
A D^{2} & =7^{2}+4^{2}-1^{2} \\
A D^{2} & =64 \\
A D & =8
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-203.jpg?height=323&width=482&top_left_y=1584&top_left_x=1301)

The area of triangle $A D C$ is thus $\frac{1}{2}(1)(8)=4$.

Therefore, the total area of quadrilateral $A B C D$ is the sum of the areas of the two triangles, or $14+4=18$.

ANSWER: (C)