Question

Find the area of each of the following triangle:

Answer 1

Hint: The space occupied by all the three sides of a triangle is called area of the triangle. Usually, we use a basic formula to calculate the area of the triangle which is stated as \[\dfrac{1}{2} \times base \times height\]. For that, we need the length of any side of the triangle and perpendicular drawn on that side from the adjacent point of the other two sides. In the above question, (a) & (b) part of the same form. Triangle given in part (c) of the question is a right-angled triangle. In a right angled triangle, other than hypotenuse (longest side of the triangle), one side is base and one side is height of the triangle itself.
Formula used:
Area of triangle =\[\dfrac{1}{2} \times base \times height\]

Complete step-by-step solution:
For triangle (a)
base = \[4cm\]
height = \[3cm\]
Area of triangle =\[\dfrac{1}{2} \times base \times height\]
Area of triangle = \[\dfrac{1}{2} \times 4cm \times 3cm\]
Area of triangle = \[6c{m^2}\]
For triangle (b)
base = \[5cm\]
height = \[3.2cm\]
Area of triangle =\[\dfrac{1}{2} \times base \times height\]
Area of triangle = \[\dfrac{1}{2} \times 5cm \times 3.2cm\]
Area of triangle = \[8c{m^2}\]
For triangle (c)
base = \[3cm\]
height = \[4cm\]
Area of triangle =\[\dfrac{1}{2} \times base \times height\]
Area of triangle = \[\dfrac{1}{2} \times 3cm \times 4cm\]
Area of triangle = \[6c{m^2}\]

Note: Here, in the above question in part (c), we were directly given two sides other than hypotenuse, but, there may be cases that we are given (i) one side and one angle, or (ii) hypotenuse and one other side. In both the cases, height can be found out using trigonometry in (i) case and Pythagoras theorem \[\left[ {{{\left( {hypotenuse} \right)}^2} = {{\left( {base} \right)}^2} + {{\left( {perpendicular} \right)}^2}} \right]\] in (ii) case.
And in case, if we are given all the sides of a triangle, we can find the area using heron’s formula.