$A$ triangle and a parallelogram have the same area. If the sides of the triangle are $10 \, cm$,$17 \, cm$,and $21 \, cm$,and the parallelogram stands on the base $12 \, cm$,find the height of the parallelogram. (in $, cm$)

In quadrilateral $ABCD$, $\angle A = 90^{\circ}$, $AB = 15 \text{ cm}$, $BC = 25 \text{ cm}$, $CD = 12 \text{ cm}$, and $DA = 8 \text{ cm}$. Find the area of quadrilateral $ABCD$. (in $\text{ cm}^2$)

In a trapezium $ABCD$, $AB \parallel CD$. If $AB = 30 \, cm$, $BC = 17 \, cm$, $CD = 20 \, cm$, and $DA = 9 \, cm$, then find its area. (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).

The sides of a triangle measure $15 \text{ cm}$,$17 \text{ cm}$,and $20 \text{ cm}$. Then,the semi-perimeter of the triangle is ......... $\text{cm}$.

In $\Delta ABC$,$AB = 20 \, cm$,$BC = 48 \, cm$,and $AC = 52 \, cm$,find the area of $\Delta ABC$. (in $, cm^2$)