Triangle Base Calculation: Finding BC When Area is 20 cm² and Height is 8

Q: Why do we divide by 2 in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half that space, so we divide by 2.

Q: Can I use this formula for any type of triangle?

Yes! The formula $ Area = \frac{base \times height}{2} $ works for all triangles - right triangles, acute triangles, and obtuse triangles.

Q: What if the height doesn't look perpendicular in the diagram?

The height is always perpendicular to the base, even if the diagram makes it look slanted. Point D shows where the height meets BC at a right angle.

Q: Can I cross-multiply to solve this?

Absolutely! From $ 20 = \frac{8 \times BC}{2} $, cross-multiplying gives $ 40 = 8 \times BC $, then divide both sides by 8.

Triangle Area Formula with Given Height

The area of triangle ABC is 20 cm².

Its height (AD) is 8.

Calculate the length of the side BC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's calculate B C.

00:14 First, examine the lengths given for the sides and lines.

00:18 Now, use the area formula for a triangle.

00:27 Multiply the height by the base, then divide by two.

00:32 Substitute the values and solve for B C.

00:37 Next, multiply by the denominator to find B C.

00:45 Isolate B C on one side of the equation.

01:13 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of triangle ABC is 20 cm².

Its height (AD) is 8.

Calculate the length of the side BC.

Step-by-step solution

We can insert the given data into the formula in order to calculate the area of the triangle:

$S=\frac{AD\times BC}{2}$

$20=\frac{8\times BC}{2}$

Cross multiplication:

$40=8BC$

Divide both sides by 8:

$\frac{40}{8}=\frac{8BC}{8}$

$BC=5$

Final Answer

5 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (base × height) ÷ 2 for any triangle
Technique: Rearrange to base = (2 × Area) ÷ height = (2 × 20) ÷ 8
Check: Verify: $\frac{5 \times 8}{2} = 20$ cm² ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't use Area = base × height directly = gives 160 cm instead of 5 cm! This misses the essential ÷2 part of the triangle area formula. Always remember that triangle area = (base × height) ÷ 2, so when solving for base, multiply area by 2 first.

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

Why do we divide by 2 in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half that space, so we divide by 2.

Can I use this formula for any type of triangle?

Yes! The formula $Area = \frac{base \times height}{2}$ works for all triangles - right triangles, acute triangles, and obtuse triangles.

What if the height doesn't look perpendicular in the diagram?

The height is always perpendicular to the base, even if the diagram makes it look slanted. Point D shows where the height meets BC at a right angle.

How do I know which side is the base?

Any side can be the base! In this problem, BC is the base because that's what we're solving for, and AD (height of 8) is perpendicular to BC.

What units should my answer have?

Since the area is in cm² and height is in cm (implied), the base will be in cm. Always use the same units as given in the problem.

Can I cross-multiply to solve this?

Absolutely! From $20 = \frac{8 \times BC}{2}$ , cross-multiplying gives $40 = 8 \times BC$ , then divide both sides by 8.

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