Area of a Triangle: Applying the formula

The triangle we are looking at is the large triangle - ABC

The triangle is formed by three sides AB, BC, and CA.

Now let's remember what we need for the calculation of a triangular area:

(side x the height that descends from the side)/2

Therefore, the first thing we must find is a suitable height and side.

We are given the side AC, but there is no descending height, so it is not useful to us.

The side AB is not given,

And so we are left with the side BC, which is given.

From the side BC descends the height AD (the two form a 90-degree angle).

It can be argued that BC is also a height, but if we delve deeper it seems that CD can be a height in the triangle ADC,

and BD is a height in the triangle ADB (both are the sides of a right triangle, therefore they are the height and the side).

As we do not know if the triangle is isosceles or not, it is also not possible to know if CD=DB, or what their ratio is, and this theory fails.

Let's remember again the formula for triangular area and replace the data we have in the formula:

(side* the height that descends from the side)/2

Now we replace the existing data in this formula:

$\frac{CB\times AD}{2}$

$\frac{11.6\times3}{2}$

$\frac{34.8}{2}=17.4$

This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.

Remember the formula for the area of a triangle:

The height is a straight line that comes out of an angle and forms a right angle with the opposite side.

In the drawing we have a height of 6.

It goes down to the opposite side whose length is 5.

And therefore, these are the data points that we will use.

We replace in the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

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

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

First, let's remember the formula for the area of a triangle:

(the side * the height that descends to the side) /2

In the question, we have three pieces of data, but one of them is redundant!

We only have one height, the line that forms a 90-degree angle - AD,

The side to which the height descends is CB,

Therefore, we can use them in our calculation:

$\frac{CB\times AD}{2}$

$\frac{8\times9}{2}=\frac{72}{2}=36$

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:

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

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

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

$\frac{BC\times AE}{2}$

We insert the existing data as shown below:

$\frac{4\times5}{2}=\frac{20}{2}=10$

To solve this problem, we'll follow these steps:

• Step 1: Identify the given dimensions: the base $BC = 8$ units, and the height $AE = 10$ units.
• Step 2: Apply the triangle area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
• Step 3: Perform the calculations using the identified dimensions.

Now, let's work through each step:

Step 1: We have the base $BC = 8$ units and the height from $A$ to $BC$, which is $AE = 10$ units.

Step 2: Using the formula for the area of a triangle, we write:

Step 3: Plugging in our values, we calculate:

Therefore, the area of the triangle is 40 square units.

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: $15.75$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given base and height.
• Step 2: Apply the formula for the area of a triangle.
• Step 3: Perform the calculation to find the area.

Now, let's work through each step:
Step 1: The base of the triangle is $6.5$ and the height is $3$.
Step 2: We'll use the formula for the area of a triangle, given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
Step 3: Plugging in our values, we get:

$\text{Area} = \frac{1}{2} \times 6.5 \times 3 = \frac{1}{2} \times 19.5 = 9.75$

Therefore, the area of the triangle is $\boxed{9.75}$.

To solve this problem, we'll use the formula for the area of a triangle given its base and height:

• Step 1: Identify the base and the height of the triangle from the given information.
• Step 2: Apply the triangle area formula.
• Step 3: Calculate the area using these values.

Now, let's apply these steps:

Step 1: From the given problem, we know:
- The base $BC$ of the triangle is $4$ units.
- The height $AE$, which is perpendicular to $BC$, is $8.5$ units.

Step 2: Use the formula for the area of the triangle:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Substitute the values into the formula:
$\text{Area} = \frac{1}{2} \times 4 \times 8.5 = 2 \times 8.5 = 17$

Hence, the area of the triangle is 17 square units.

To solve for the area of a triangle when the base and height are given, we'll use the formula:

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

Given:

• Base = $4$ units

• Height = $7$ units

Apply the formula:

$\begin{aligned} \text{Area} &= \frac{1}{2} \times 4 \times 7 \\ &= \frac{1}{2} \times 28 \\ &= 14 \end{aligned}$

Thus, the area of the triangle is $14$ square units.

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

• Step 1: Identify the given base and height from the problem.
• Step 2: Apply the formula for the area of a triangle.
• Step 3: Calculate the area by substituting the values into the formula.

Let's work through the problem:

Step 1: The base $|AB|$ of the triangle is given as 8 units, and the height $|BC|$ is 6 units.

Step 2: The formula for the area of a triangle is:

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

Step 3: Substitute the given values into the formula:

$A = \frac{1}{2} \times 8 \times 6$

Perform the multiplication:

$A = \frac{1}{2} \times 48 = 24$

Therefore, the area of the triangle is $\mathbf{24}$ square units.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: We are given that $AC = 9$ (the height) and $BC = 10$ (the base) of the triangle.

Step 2: We'll use the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

Step 3: Plugging in our values, we have:

Therefore, the area of the triangle is $45$.

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 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.

To solve this problem, we'll follow these steps:

• Step 1: Identify the base and height of the triangle.
• Step 2: Substitute these values into the formula for the area of a triangle.
• Step 3: Perform the calculation to determine the area.

Let's work through each step:

Step 1: From the given information, the base of the triangle is 7 units, and the height is 4 units.

Step 2: We'll use the formula for the area of a triangle:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Plugging in the values for the base and height, we have:
$\text{Area} = \frac{1}{2} \times 7 \times 4$

Performing the multiplication, we get:
$\text{Area} = \frac{1}{2} \times 28 = 14$

Therefore, the area of the triangle is $\textbf{14}$ square units.

To solve this problem, we will determine the area of the triangle using the given base and height. Here are the steps:

• Identify the given base and height: base $= 6$, height $= 3.5$.
• Apply the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
• Substitute the given values into the formula: $\text{Area} = \frac{1}{2} \times 6 \times 3.5$.
• Calculate the area: $= \frac{1}{2} \times 21 = 10.5$.

Therefore, the area of the triangle is $10.5$, which matches the correct multiple-choice option provided.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given base and height of the triangle.
• Step 2: Apply the formula for the area of a triangle.
• Step 3: Perform the necessary calculations to find the area.

Now, let's work through each step:
Step 1: The base of the triangle is given as 7 units, and the height is given as 5 units.
Step 2: We'll use the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
Step 3: Plugging in our values, we have:
$\text{Area} = \frac{1}{2} \times 7 \times 5 = \frac{1}{2} \times 35 = 17.5$.

Therefore, the area of the triangle is $17.5$ square units.

To solve this problem, we will follow these steps:

• Step 1: Identify the relevant sides based on problem context
• Step 2: Apply the standard triangle area formula
• Step 3: Calculate the area based on the known values for base and height

Let's work through each step in detail:

Step 1: We are seeking to calculate the area of the triangle. We identified that the line segment of 4 units represents the height, and the base is 7 units.

Step 2: We will apply the formula for the area of a right triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

Step 3: Plug the values we have: $\text{Area} = \frac{1}{2} \times 7 \times 4 = \frac{1}{2} \times 28 = 14$.

Thus, the area of the triangle is $14$ square units.