Find the area of a triangle two sides of which are $18 \, cm$ and $10 \, cm$ and the perimeter is $42 \, cm$.

$A$ design is made on a rectangular tile of dimensions $50\, cm \times 70\, cm$ as shown in the figure. The design shows $8$ triangles,each with sides $26\, cm, 17\, cm$,and $25\, cm$. Find the total area of the design and the remaining area of the tile.

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 $5 \, cm$.

$A$ triangular park $ABC$ has sides $120\,m, 80\,m$ and $50\,m$ (see Fig.). $A$ gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of $Rs. 20$ per metre leaving a space $3\,m$ wide for a gate on one side.

Write True or False and justify your answer.
In a triangle,the sides are given as $11 \, cm$,$12 \, cm$,and $13 \, cm$. The length of the altitude corresponding to the side of length $12 \, cm$ is $10.25 \, cm$.

Find the area of a quadrilateral $ABCD$ in which $AB = 3 \, cm, BC = 4 \, cm, CD = 4 \, cm, DA = 5 \, cm$ and $AC = 5 \, cm$. (in $, cm^2$)