Area of a Triangle: Using decimal fractions

To solve this problem, follow these steps:

• Step 1: Identify the base $AB$ and height $AC$ of the triangle.

• Step 2: Apply the formula for the area of a right triangle.

• Step 3: Calculate the area using the given measurements.

Now, let's proceed:

Step 1: From the problem, the base $AB = 3.5$ units, and the height $AC = 4.6$ units.
Step 2: The area $A$ of a right triangle is given by the formula:
$A = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Plug in the values:
$A = \frac{1}{2} \times 3.5 \times 4.6$
$A = \frac{1}{2} \times 16.1$
$A = 8.05$

Therefore, the area of the triangle is $\textbf{8.05}$ square units.

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

• Step 1: Identify the given information:
• The base of the triangle is $7.8$ units.
• The height of the triangle is $5.5$ units.
• Step 2: Apply the formula for the area of a right triangle:

The formula for the area of a triangle is:

Step 3: Perform the necessary calculations:

Substitute the values we have:

Calculating further:

Therefore, the area of the triangle is $21.45$ square units.

This matches with choice 4 provided: 21.45.

To solve this problem, let's follow these steps:

• Step 1: Identify the given information: The area $A = 8.375$, one side $a = X$, and the other side $b = 2.5$.
• Step 2: Utilize the formula for the area of a right triangle, $A = \frac{1}{2} \times \text{base} \times \text{height}$.
• Step 3: Plug in the known values to the formula and solve for $X$.

Detailed solution:

We have the area formula for a right triangle:

Substitute the given area value:

Let's rearrange this equation to solve for $X$:

Calculate:

Therefore, the length of side $X$ is $\mathbf{6.7}$.

This corresponds to choice 2: 6.7

To find the missing side $X$ of the triangle:

• Step 1: Identify the given values: area $A = 18.5$ and height $h = 10$.
• Step 2: Use the area formula for a triangle: $A = \frac{1}{2} \times \text{base} \times \text{height}$.
• Step 3: Plug in the known values into the formula:
  $18.5 = \frac{1}{2} \times X \times 10$.
• Step 4: Simplify and solve for $X$:
  $18.5 = 5 \times X$
  Divide both sides by 5 to isolate $X$:
  $X = \frac{18.5}{5}$.
• Step 5: Calculate $X$:
  $X = 3.7$.

Therefore, the missing side $X$ is $3.7$.

To solve this problem, we need to determine $X$ using the triangle area formula. Let's break it down step-by-step:

• Step 1: The area of a triangle $\Delta ABC$ is given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
• Step 2: We substitute the given values where the base is $(X + 6)$ and the height is $5$: $22.5 = \frac{1}{2} \times (X + 6) \times 5$
• Step 3: Simplify the equation: $22.5 = \frac{1}{2} \times 5 \times (X + 6)$
• Step 4: Multiply out the constants: $22.5 = \frac{5}{2} \times (X + 6)$
• Step 5: Clear the fraction by multiplying both sides by 2: $45 = 5 \times (X + 6)$
• Step 6: Divide both sides by 5: $9 = X + 6$
• Step 7: Solve for $X$: $X = 9 - 6 = 3$

Therefore, the solution to the problem is $X = 3$.