Question

question 14 of 25
which expression gives the area of the triangle shown below?
image of a right triangle with height x, base c, and other sides a, b
a. \\(\frac{1}{2}cx\\)
b. \\(\left(\frac{1}{2}a\
ight)\left(\frac{1}{2}c\
ight)\\)
c. \\(\left(\frac{1}{2}c\
ight)\left(\frac{1}{2}x\
ight)\\)
d. \\(\frac{1}{2}ac\\)

Explanation:

Step1: Recall Triangle Area Formula

The area of a triangle is given by $\frac{1}{2} \times \text{base} \times \text{height}$.

Step2: Identify Base and Height

In the right - angled triangle (from the diagram, the right angle is at the intersection of the base of length $c$ and the height of length $x$), the base is $c$ and the height is $x$.

Step3: Apply the Formula

Substituting the base $c$ and height $x$ into the area formula $\frac{1}{2}\times\text{base}\times\text{height}$, we get the area as $\frac{1}{2}cx$.

Answer:

A. $\frac{1}{2}cx$