Area of a Triangle Practice Problems and Solutions

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 solve the problem of finding the area of triangle $\triangle ABC$, we follow these steps:

• Step 1: Identify the given measurements.
• Step 2: Use the appropriate formula for the area of a triangle.
• Step 3: Calculate the area using these measurements.

Let's go through each step in detail:
Step 1: From the figure, the base $AB = 10$ and height $AC = 2$.
Step 2: The formula for the area of a triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
Step 3: Substituting the known values into the formula, we get:

$\text{Area} = \frac{1}{2} \times 10 \times 2 = \frac{1}{2} \times 20 = 10$

Therefore, the area of triangle $\triangle ABC$ is 10.

To solve this problem, we begin by analyzing the given triangle in the diagram:

While the triangle graphic suggests some line segments labeled with the values "7.6" and "4", it does not confirm these as directly usable as pure base or height without additional proven inter-contextual relationships establishing perpendicularity or side/unit equivalences.

Without a clear base and perpendicular height value, we cannot apply the triangle's area formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ effectively, nor do we have all side lengths for Heron's formula.

Therefore, due to insufficient information that specifically identifies necessary dimensions for area calculations such as clear height to a base or all sides' measures, the area of this triangle cannot be calculated.

The correct answer to the problem, based on insufficient explicit calculable details, is: It cannot be calculated.

The formula to calculate the area of a triangle is:

(side * height corresponding to the side) / 2

Note that in the triangle provided to us, we have the length of the side but not the height.

That is, we do not have enough data to perform the calculation.

The formula for the area of a triangle is

$A = \frac{h\cdot base}{2}$

Let's insert the available data into the formula:

(7*6)/2 =

42/2 =

21