Calculate Triangle Height PQ Given Area 30 cm² and Base 4 cm

Q: Why is the height drawn outside the triangle in the diagram?

In an obtuse triangle, the height from the obtuse angle vertex falls outside the triangle. This is normal! The perpendicular distance from point P to line SR is still the height, even if it's outside.

Q: Can I use any side as the base?

Yes! You can use any side as the base, but then you must use the corresponding height (perpendicular to that base). In this problem, we're given SR = 4 cm as the base and asked for height PQ.

Q: What if I get the area formula backwards?

If you use $ \text{Area} = \frac{\text{height} \times \text{base}}{2} $ instead of $ \text{Area} = \frac{\text{base} \times \text{height}}{2} $, it's the same thing! Multiplication is commutative, so base × height = height × base.

Q: How do I know which measurement is the height?

The height is always the perpendicular distance from a vertex to the opposite side (or its extension). Look for the right angle symbol (small square) in the diagram - that shows where the height meets the base.

Q: Can the height be longer than the sides of the triangle?

Absolutely! In obtuse triangles, the height can be longer than some sides. There's no rule limiting height length - it depends on the triangle's shape and area.

Triangle Area Formula with Height Calculation

PRS is a triangle.

The length of side SR is 4 cm.
The area of triangle PSR is 30 cm².

Calculate the height PQ.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's calculate the height P Q.

00:14 Look at the lengths of the sides and lines using the given data.

00:18 Now, use the formula to find the area of a triangle.

00:26 It's height times base, all divided by two.

00:31 Plug in the values and solve for P Q.

00:39 Multiply by the denominators to clear any fractions.

00:49 Now, isolate P Q on one side.

01:05 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

PRS is a triangle.

The length of side SR is 4 cm.
The area of triangle PSR is 30 cm².

Calculate the height PQ.

Step-by-step solution

We use the formula to calculate the area of the triangle.

Pay attention: in an obtuse triangle, the height is located outside of the triangle!

$\frac{Side\cdot Height}{2}=\text{Triangular Area}$

Double the equation by a common denominator:

$\frac{4\cdot PQ}{2}=30$

$\cdot2$

Divide the equation by the coefficient of $PQ$ .

$4PQ=60$ / $:4$

$PQ=15$

Final Answer

15 cm

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area = (base × height) ÷ 2 for all triangles
Rearrangement: height = (2 × Area) ÷ base = (2 × 30) ÷ 4
Check: Verify: (4 × 15) ÷ 2 = 30 cm² matches given area ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply area by 2 when solving for height
Don't use height = Area ÷ base = 30 ÷ 4 = 7.5 cm! This ignores the division by 2 in the area formula and gives half the correct answer. Always rearrange the complete formula: height = (2 × Area) ÷ base.

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 is the height drawn outside the triangle in the diagram?

In an obtuse triangle, the height from the obtuse angle vertex falls outside the triangle. This is normal! The perpendicular distance from point P to line SR is still the height, even if it's outside.

Can I use any side as the base?

Yes! You can use any side as the base, but then you must use the corresponding height (perpendicular to that base). In this problem, we're given SR = 4 cm as the base and asked for height PQ.

What if I get the area formula backwards?

If you use $\text{Area} = \frac{\text{height} \times \text{base}}{2}$ instead of $\text{Area} = \frac{\text{base} \times \text{height}}{2}$ , it's the same thing! Multiplication is commutative, so base × height = height × base.

How do I know which measurement is the height?

The height is always the perpendicular distance from a vertex to the opposite side (or its extension). Look for the right angle symbol (small square) in the diagram - that shows where the height meets the base.

Can the height be longer than the sides of the triangle?

Absolutely! In obtuse triangles, the height can be longer than some sides. There's no rule limiting height length - it depends on the triangle's shape and area.

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