Find the base of a triangle whose area is \[360c{m^2}\] and height is \[24cm\]

Hint: The area of any triangle is defined as the total area enclosed by its all three sides. Generally, the area of any triangle is equal to the half of the product of its length of the base and the height of the triangle. So for determining the area of a triangle we have to put values and we will get the area of the given triangle.

Formula used:
Area of triangle\[ = \dfrac{1}{2} \times base \times height\]
Given: Area of the given triangle=\[360c{m^2}\]& height of the triangle=\[24cm\]
To find: Using the given information we have to find the length of the base of the triangle

Complete step-by-step solution:
Step 1: Since we have the value of area of the given triangle and the value of its height, therefore we use such a type of formula so that we can use the given information and determine the value of the unknown term.
As we know that the area of triangle is given by,
Area of triangle\[ = \dfrac{1}{2} \times base \times height\]
Now, substituting the value in above formula, we get
\[360 = \dfrac{1}{2} \times base \times 24\]
Step 2: Taking base to one side and all other known values to other side, we get
\[base = 360 \times 2 \times \dfrac{1}{{24}}\]
Step 3: After multiplication, we get
\[ \Rightarrow \]\[base = 360 \times 2 \times \dfrac{1}{{24}}\]
\[ \Rightarrow \]\[base = 720 \times \dfrac{1}{{24}}\]
\[ \Rightarrow \]\[base = 30\]cm
Hence, the length of base of the given triangle is equal to \[30cm\] .

Note: If height and base of the triangle are known then the area of triangle is given by Area of triangle\[ = \dfrac{1}{2} \times base \times height\]
When all the three sides of the triangle are given then the area of the triangle is given by Heron’s formula
\[Area = \sqrt {s(s - a)(s - b)(s - c)} \]
\[s = \] Semi perimeter of triangle
\[a,b\& c\] are length of the sides of the triangle