Area of a Triangle Practice Problems & Step-by-Step Solutions

To solve this problem, begin by identifying the elements involved in calculating the area of a right triangle. In a right triangle, the two sides that form the right angle are known as the legs. These legs act as the base and height of the triangle.

The formula for the area of a triangle is given by:

In the case of a right triangle, the base and height are the two legs. Therefore, the process of finding the area involves multiplying the lengths of the two legs together and then dividing the product by 2.

Based on this analysis, the correct way to complete the sentence in the problem is:

To find the area of a right triangle, one must multiply the two legs by each other and divide by 2.

Due to the fact that AB is perpendicular to BC and forms a 90-degree angle,

it can be argued that AB is the height of the triangle.

Hence we can calculate the area as follows:

$\frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24$

To find the area of the triangle, we will use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

From the problem:

• The length of the base $BC$ is given as 7 units.
• The height from point $A$ perpendicular to the base $BC$ is given as 4.5 units.

Substitute the given values into the area formula:

$\text{Area} = \frac{1}{2} \times 7 \times 4.5$

Calculate the expression step-by-step:

$\text{Area} = \frac{1}{2} \times 31.5$

$\text{Area} = 15.75$

Therefore, the area of the triangle is $15.75$ square units. This corresponds to the given choice: $15.75$.

First, we will identify the data points we need to be able to find the area of the triangle.

the formula for the area of the triangle: height*opposite side / 2

Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.

We multiply the legs and divide by 2

$\frac{5\times7}{2}=\frac{35}{2}=17.5$

To calculate the area of the triangle, we will follow these steps:

• Identify the base, CB, as 6 units.
• Identify the height, AC, as 8 units.
• Apply the area formula for a triangle.

Now, let's work through these steps:

The triangle is a right triangle with base $CB = 6$ units and height $AC = 8$ units.

The area of a triangle is determined using the formula:

Substituting the known values, we have:

Perform the multiplication and division:

Therefore, the area of the triangle is $24$ square units.