Q64. - Algebra 1

Question

GEOMETRY Find the area of $\Delta ABC$ if each small triangle has a base of 5.2 inches and a height of 4.5 inches. (Lesson 1 - 3)

Step-by-Step Solution

Answer

The area of triangle ABC is $46.8 {\text{inches}}^{\text{2}}$.

Step 1. Find the height of the triangle.

We are given that the height of the small triangle is 4.5 inches.

The height of triangle ABC will be two times the height of the small triangle, thus:

$\begin{array}{l}\text{Height of ΔABC}=4.5\times 2\\ =9 \text{inches}\end{array}$

Step 2. Find the base of triangle.

We are given that the base of a small triangle is 5.2 inches.

The base of triangle ABC will be two times the height of the small triangle, thus:

$\begin{array}{l}\text{Base of ΔABC}=5.2\times 2\\ =10.4\text{ inches}\end{array}$

Step 3. Find the area of a triangle.

We are given that the base of the triangle is 9 inches.

And the height of the triangle is 104. inches.

Are of the triangle is half of the product of the height and base of the triangle.

Thus, the area of the triangle will be:

$\begin{array}{l}=\frac{1}{2}\times 10.4\times 9\\ =\frac{93.6}{2}\\ =46.8{\text{inches}}^{\text{2}}\end{array}$