Question

There is a slide in a children’s park. The front side of the park has been painted and a message ONLY FOR CHILDREN is written on as shown in the figure. If the sides of the triangular front wall of the side are$9m,8m\& 3m$, then find the area which is painted in color.

Answer 1

Hint: In the given question first we will consider the diagram which is already given in the question, a triangle is given whose all three sides are unequal called the scalene triangle. As we know that there is a formula to find the area of a triangle whose all sides are unequal, we will apply the formula and calculate the area of the given triangle. First we will find the perimeter which is denoted by s of the given triangle i.e. \[s = \dfrac{{a + b + c}}{2}\] , and then we will apply the formula of area of triangle i.e. $\sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} $ Thus we will get the correct answer.
Formula: Area of triangle= $\sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} $
Where s is the perimeter of the triangle.

Complete step by step Answer:

Consider the given diagram:

Let three sides of the triangle are $a,b,c$
Where
$
  a = 9m \\
  b = 8m \\
  c = 3m \\
 $
First we will calculate the perimeter of the given triangle:
As we know the formula of perimeter is:
\[s = \dfrac{{a + b + c}}{2}\]
Put the values of $a,b,c$in the above formula:
We get:
$
   \Rightarrow s = \dfrac{{9 + 8 + 3}}{2} \\
   \Rightarrow s = \dfrac{{20}}{2} \\
   \Rightarrow s = 10m \\
 $
Now we have fins the perimeter of the triangle which is $s = 10m$
Now apply the formula to find the area of triangle:
Which is:
Area of triangle= $\sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} $
Now put the values of $s,a,b,c$ in the above formula:
We get:
Area of triangle is
$
   \Rightarrow \sqrt {10\left( {10 - 9} \right)\left( {10 - 8} \right)\left( {10 - 3} \right)} \\
   \Rightarrow \sqrt {10 \times 1 \times 2 \times 7} \\
   \Rightarrow \sqrt {140} \\
   \Rightarrow 2\sqrt {35} {m^2} \\
 $
Hence the correct answer is option A.

Note: First of all we have to learn and remember the property of this type of triangle whose all sides are unequal called the scalene triangle. We have to remember the formula to find the perimeter and area of the triangle, and then apply both formulas in the given question.