Question

Segment BD is an altitude of triangle ABC. Find the area of the triangle

Answer 1

Answer:

The area of triangle ABC is A. 7.5.

Step-by-step explanation:

There are three sides in triangle ABC: AB, BC, and AC. However, only side AC is perpendicular to altitude BD. Therefore, BD is the altitude on base AC.

Refer to the scales on the two axes. The length of each grid square's side is equal to 1. Segment BD spans three such sides; the length of BD is thus 3. Similarly, the length of segment AC is 5 for it spans five such sides.

$\begin{aligned}&\text{Area of a Triangle}\\ =&\frac{1}{2}\; \text{Base} \times \text{Height on that Base}\end{aligned}$.

For this question,

$\begin{aligned}&\text{Area of a Triangle ABC}\\ =&\frac{1}{2}\; \text{Base AC} \times \text{Height on Base AC} \\ =& \frac{1}{2}\; \text{Length of Segment AC}\times \text{Length of Segment BD}\\ =&\frac{1}{2}\times5\times 3= \frac{15}{2} =7.5\end{aligned}$.