Question

question 21 of 25 which expression gives the area of the triangle shown below? image of a triangle with a vertical dashed line labeled ( x ) (height), a horizontal dashed line labeled ( c ) (base), and sides labeled ( a ), ( b )

options:

a. ( \frac{1}{2}cx )

b. ( left( \frac{1}{2}a
ight) left( \frac{1}{2}c
ight) )

c. ( \frac{1}{2}ac )

d. ( left( \frac{1}{2}c
ight) left( \frac{1}{2}x
ight) )

Explanation:

Step1: Recall triangle area formula

The formula for the area of a triangle is $A = \frac{1}{2} \times \text{base} \times \text{height}$.

Step2: Identify base and height

In the given triangle, the base is $c$ (the horizontal side) and the height is $x$ (the vertical dashed line, perpendicular to the base).

Step3: Substitute into formula

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

Answer:

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