A K Upadhyay and S Upadhyay Solutions for Chapter: Heron's Formula, Exercise 3: TEST YOURSELF

If the area of a triangle is $k\sqrt{30} {\mathrm{cm}}^2$, two sides of which are $8 \mathrm{c}\mathrm{m}$ and $11 \mathrm{c}\mathrm{m}$ and its perimeter is $32 \mathrm{c}\mathrm{m}$. Find the value of $k$.

Find the area of a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ in which $\mathrm{A}\mathrm{B}=9 \mathrm{m},\mathrm{B}\mathrm{C}=40 \mathrm{m},\mathrm{C}\mathrm{D}=15 \mathrm{m},\mathrm{\angle }\mathrm{B}=90°$ and $\mathrm{D}\mathrm{A}=28 \mathrm{m}$.

The adjacent sides of a parallelogram are $36 \mathrm{c}\mathrm{m}$ and $27 \mathrm{c}\mathrm{m}$ in length. If the distance between the shorter sides is $12 \mathrm{c}\mathrm{m}$. If the distance between the longer sides is $h \mathrm{cm}$, find the value of $h$.

The base of an isosceles triangle measure $24 \mathrm{c}\mathrm{m}$ and its area is $192 \mathrm{c}{\mathrm{m}}^2$. If its perimeter is $k \mathrm{cm}$, find the value of $k$.

If the area of a trapezium whose parallel sides $11 \mathrm{m}$ and $25 \mathrm{m}$ long and the non-parallel sides are $15 \mathrm{m}$ and $13 \mathrm{m}$ long is $k {\mathrm{m}}^2$, find the value of $k$.

A rhombus shaped field has been green grass for $18$ cows to graze. If each side of the rhombus is $30 \mathrm{m}$ and its longer diagonals is $48 \mathrm{m}$. If the area of grass field each cow gets is $k {\mathrm{m}}^2$, find the value of $k$

A kite in the shape of a square with a diagonal $32 \mathrm{c}\mathrm{m}$ and an isosceles triangle of base $8 \mathrm{c}\mathrm{m}$ and side $6 \mathrm{c}\mathrm{m}$ each is to be made of three different shades as shown is Figure. How much paper of each shade has been used in it.

The sides of the triangular plot are in the ratio of $3:5:7\mathrm{}$ and its perimeter is $300 \mathrm{m}$. If its area is $k\sqrt{3} {\mathrm{m}}^2$, find the value of $k$.