Finding the Area of an Acute Triangle

$A=\frac{1}{2}bh$

The base, $b$, is $6$ feet and the height, $h$ is $4$ feet.

$A=\frac{1}{2}(6)(4)$

$A=12$ ft$^2$

To find the area, we identify the base as 4 metres and the height as 3 metres. Using the formula $A = \frac{1}{2}bh$, we substitute the values: $A = \frac{1}{2}(4)(3) = 6 \text{ metres}^2$. Therefore, the area of the triangle is $6 \text{ metres}^2$.

First, identify the base and height: the base is 5 feet and the height is 8 feet. Using the formula $A = \frac{1}{2}bh$, the calculation is $A = \frac{1}{2}(5)(8) = 20 \text{ cm}^2$. The area of the triangle is $20 \text{ cm}^2$.

The base is 10 centimetres and the height is 14 centimetres. Applying the formula $A = \frac{1}{2}bh$, we get $A = \frac{1}{2}(10)(14) = 70 \text{ cm}^2$. Thus, the area of the triangle is $70 \text{ cm}^2$.

By identifying the base as 2 metres and the height as 5 metres, and using $A = \frac{1}{2}bh$, the area calculation is $A = \frac{1}{2}(2)(5) = 5 \text{m}^2$. So, the triangle's area is $5 \text{ m}^2$.

With the base at 6 feet and the height at 2 feet, using the formula $A = \frac{1}{2}bh$, we find $A = \frac{1}{2}(6)(2) = 6 \text{ ft}^2$. The area of this acute triangle is $6 \text{ ft}^2$.

Given a base of 7 inches and a height of 4 inches, the area is calculated as $A = \frac{1}{2}(7)(4) = 14 \text{ in}^2$. Hence, the triangle's area is $14 \text{ in}^2$.

Use the formula $A = \frac{1}{2}bh$. $A = \frac{1}{2} \times 8m \times 5m = 20m²$. You have 20 square metres of planting area.

Applying $A = \frac{1}{2}bh$ gives us: $A = \frac{1}{2} \times 6cm \times 10cm = 30cm²$. The sail's area is 30 square centimetres, perfect for your model boat!

Using the formula, we find: $A = \frac{1}{2} \times 50cm \times 75cm = 1875cm²$. You will need 1875 square centimetres of material to make your kite.

Solving for Base or Height When Area is Known

Sometimes, you might know the area of an acute triangle and either it's base or height but need to find the missing dimension. To solve for the missing dimension, you can rearrange the formula for the area of a triangle, $A = \frac{1}{2}bh$, where $A$ is the area, $b$ is the base, and $h$ is the height.

• If the base is known and you need to find the height:
  • Use the formula $h = \frac{2A}{b}$.
• If the height is known and you need to find the base:
  • Use the formula $b = \frac{2A}{h}$.

Suppose you know an acute triangle has an area of $50$ square units and a base of $10$ units. To find the height, rearrange the area formula to solve for $h$:

• $h = \frac{2A}{b} = \frac{2 \times 50}{10} = 10$ units.

Imagine you have an acute triangle with an area of $36$ square units and a height of $9$ units. To find the base, rearrange the formula:

• $b = \frac{2A}{h} = \frac{2 \times 36}{9} = 8$ units.

Learning how to find the base or height of an acute triangle when you know its area helps you solve real-life problems in geometry and engineering, making you better at figuring out missing measurements.

An acute triangle is a triangle where all three internal angles are less than 90 degrees.

The area of an acute triangle is calculated using the formula $A = \frac{1}{2}bh$, where $b$ is the base length and $h$ is the height perpendicular to the base.

Yes, any side of an acute triangle can be considered the base when calculating the area, as long as the height is perpendicular to it.

The height can be found by drawing a perpendicular line from the base to the opposite vertex. In some cases, you may need to use other geometric properties or the Pythagoras’ theorem to calculate it.

No, the formula $A = \frac{1}{2}bh$ is used to calculate the area of any triangle, not just acute triangles.

Knowing how to calculate the area of an acute triangle is crucial for understanding geometric principles, solving practical problems in real life and progressing in the study of mathematics.

Using the wrong height, one that is not perpendicular to the chosen base, will result in an incorrect calculation of the triangle's area.

Yes, the area formula can be applied to triangles on a coordinate plane as long as you can determine the base and the perpendicular height.

The area should be expressed in square units, based on the units used for the base and height. For example, if the base and height are in centimetres, the area will be in square centimetres.

The area formula $A = \frac{1}{2}bh$ applies regardless of the side lengths. As long as you correctly identify the base and its corresponding perpendicular height, you can accurately calculate the area.