Area of Polygons: Triangle Formulas | List of Area of Polygons: Triangle Formulas You Should Know - BYJUS

# Area of Polygons: Triangle Formulas

The area is defined as the measure of space occupied by a shape in a two-dimensional plane. Objects around us like traffic signs, triangular roofs, pizza and so on, have a specific area. There are different formulas to calculate the area of different types of triangles. Here we will focus on the formula used to calculate the area of a triangle in terms of its base and height....Read MoreRead Less

### Area of the Triangle Formula

We can use the following formula to calculate the area of a triangle:

• Area of triangle A = $$\frac{1}{2}$$ × b × h

We will discuss this formula in detail in the next section.

### How do we use the area of a triangle formula?

To calculate the area of a triangle, you need the measure of its base and height.

As we just saw, the area (A) of a triangle is one-half of the product of its base (b) and height (h).

Mathematically, the area of a triangle can be expressed as:

Area of triangle A = $$\frac{1}{2}$$ × b× h Where,

b =  base of a triangle

h =  height of a triangle.

The area is measured in square units.

[Note : The base and the height are perpendicular to each other.]

### Solved Examples

Example 1: Find the area of the triangle whose base is 7 inches long and height is 14 inches.

Solution:

$$A=\frac{1}{2}\times b \times h$$               Area of a triangle formula

$$~~~=\frac{1}{2}\times 7 \times (14)$$          Substitute values of b and h

$$~~~=\frac{1}{2}\times (98)$$                 Multiply

$$~~~= 49$$                           Simplify

Hence, the area of the triangle is 49 square inches.

Example 2: The area of the triangle is 94 sq.mm. Find the height of the triangle if the base is 12 mm long.

Solution:

The area of the triangle is 94 sq.mm and the base is 12 mm. Therefore, we use the area of a triangle formula to form an equation to find height,

$$\frac{1}{2}\times b \times h = A$$                Area of a triangle formula

$$\frac{1}{2}\times (12) \times h = 94$$          Substitute values of b and A

$$(12) \times h = 188$$               Multiply both sides by 2

$$h=\frac{188}{12}$$                           Divide both sides by 12

$$h\approx$$ 15.67

Hence, the height of the triangle is approximately 15.67 mm.

Example 3: The area of the triangle is 25 sq.ft . Find the base of the triangle if the height is 5 ft long.

Solution:

The area of the triangle is 25 sq.ft and the height is 5 sq.ft. Therefore, we use the area of a triangle formula to form an equation to find the base,

$$\frac{1}{2}\times b \times h = A$$               Area of a triangle formula

$$\frac{1}{2}\times b \times (5) = 25$$           Substitute values of h and A

$$b \times (5) = 50$$                   Multiply both sides by 2

$$b=\frac{50}{5}$$                            Divide both sides by 5

$$b = 10$$

Hence, the base of the triangle is 10 ft .

Example 4: Find the measure of the unknown side. Solution:

The unknown side is the height, h, of the triangle.

The area of the triangle is 90 sq.ft and the base is 15 ft. Therefore, we use the area of a triangle formula to form an equation to find the height,

$$\frac{1}{2}\times b \times h = A$$                Area of a triangle formula

$$\frac{1}{2}\times 15 \times h = 90$$             Substitute values of b and A

$$(15) \times h = 180$$               Multiply both sides by 2

$$h=\frac{180}{15}$$                           Divide both sides by 15

$$h = 12$$

Hence, the height of the triangle is 12 ft.

Example 5: Larry has bought a piece of land in a village and it is in the shape of a triangle as shown in the diagram. How many square yards of land did Larry buy? Solution:

We will use the area of triangle formula to find the the number of square yards of land bought by Larry,

$$A=\frac{1}{2}\times b \times h$$                Area of a triangle formula

$$~~~=\frac{1}{2} \times 35 \times (30)$$         Substitute values of b and h

$$~~~=\frac{1}{2}\times 1050$$                 Multiply

$$~~~= 525$$                          Simplify

Hence, Larry bought 525 square yards of land.

The sum of the measures of all three sides of a triangle is the perimeter of the triangle.

A triangle in which all three sides are of different lengths is a scalene triangle.

A figure formed by combining triangles, rectangles and any other type of polygon is called a composite figure.

Example: Any side of a triangle can be taken as its base when calculating its area.