The base of a right triangle is $8 \, cm$ and its hypotenuse is $10 \, cm$. Its area will be (in $cm^2$):

In a right-angled triangle,the length of the hypotenuse is $29\,cm$ and one of the sides forming the right angle is $21\,cm$. Then,the semi-perimeter of the triangle is ............ $cm$.

The sides of a triangle are $56 \ cm$,$60 \ cm$,and $52 \ cm$ long. Then the area of the triangle is (in $cm^2$)

Students of a school staged a rally for a cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes $AB, BC$ and $CA$; while the other through $AC, CD$ and $DA$ (see Fig.). Then they cleaned the area enclosed within their lanes. If $AB = 9 \, m, BC = 40 \, m, CD = 15 \, m, DA = 28 \, m$ and $\angle B = 90^{\circ}$,which group cleaned more area and by how much (in $, m^2$)? Find the total area cleaned by the students (neglecting the width of the lanes).

Write True or False and justify your answer.
The area of the isosceles triangle is $\frac{5}{4} \sqrt{11} \, cm^2$,if the perimeter is $11 \, cm$ and the base is $5 \, cm$.

Find the cost of laying grass in a triangular field of sides $50 \, m$,$65 \, m$,and $65 \, m$ at the rate of $Rs \, 7$ per $m^2$ (in $Rs$).