Home / United States / Math Classes / Formulas / 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

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.

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.]

**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.

Frequently Asked Questions

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.