Calculate Triangle Height DH Using Area 60 cm² and Base 12 units

Question

The area of the triangle DEF is 60 cm².

The length of the side FE = 12.

Calculate the height DH.

00:00 Calculate the height DH

00:03 Observe the sides and lines according to the given data

00:08 Apply the formula for calculating the area of a triangle

00:18 (height x base) divided by 2

00:22 Insert the relevant values and proceed to solve for DH

00:43 Multiply by denominators in order to eliminate the fractions

00:53 Isolate DH

01:18 This is the solution

To solve this problem, we'll use the formula for the area of a triangle:

Step 1: Write the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 2: Substitute the given values: $60 = \frac{1}{2} \times 12 \times \text{DH}$ .
Step 3: Simplify the equation by calculating the half of the base: $\frac{1}{2} \times 12 = 6$ .
Step 4: Replace and solve the equation: $60 = 6 \times \text{DH}$ .
Step 5: Isolate $\text{DH}$ by dividing both sides by 6: $\text{DH} = \frac{60}{6}$ .
Step 6: Calculate the result: $\text{DH} = 10$ .

The height from point D to the base FE, $\text{DH}$ , is 10 cm.

10 cm