Calculate Area of Triangle with Base and Height

To find the area of a triangle when the base and corresponding height are known, we use a standard formula. The area of a triangle is defined as half the product of its base and its height.

The formula for the area of a triangle is:

$$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$

In this problem, we are given:

• Base of the triangle = 7 cm
• Corresponding height of the triangle = 12 cm

Now, let's substitute these values into the area formula:

$$ \text{Area} = \frac{1}{2} \times 7 \, \text{cm} \times 12 \, \text{cm} $$

Let's perform the multiplication:

First, multiply the base and height:

$$ 7 \times 12 = 84 $$

So, the formula becomes:

$$ \text{Area} = \frac{1}{2} \times 84 \, \text{cm}^2 $$

Now, multiply by \( \frac{1}{2} \) (or divide by 2):

$$ \text{Area} = \frac{84}{2} \, \text{cm}^2 $$

$$ \text{Area} = 42 \, \text{cm}^2 $$

Thus, the area of the triangle with a base of 7 cm and a height of 12 cm is 42 square centimeters.

Revision Table: Triangle Area Calculation

Additional Information: Understanding Triangle Area

The area of a triangle is a measure of the space enclosed by its three sides. The formula \( \frac{1}{2} \times \text{base} \times \text{height} \) is applicable to all types of triangles, whether they are acute, obtuse, or right-angled. The 'height' in this formula must be the perpendicular distance from the vertex opposite the chosen 'base' to the base (or its extension).

For a right-angled triangle, if one of the perpendicular sides is taken as the base, the other perpendicular side is the height. For other triangles, you might need to draw an altitude (the perpendicular line segment from a vertex to the opposite side) to determine the height.

Understanding the concept of base and corresponding height is crucial for correctly applying the area formula. The base can be any side of the triangle, but the height must be measured perpendicular to that specific base.