Jammu and Kashmir Board Solutions for Chapter: Mensuration, Exercise 7: Exercise

The diagonal of a quadrilateral shaped field is $24 \mathrm{m}$ and the perpendiculars dropped on it from the remaining opposite vertices are $13 \mathrm{m}$ and $8 \mathrm{m}$. If the area of field is $k {\mathrm{m}}^2$. Find the value of $k$.

The diagonals of a rhombus are $7.5 \mathrm{c}\mathrm{m}$ and $12 \mathrm{c}\mathrm{m}.$ If its area is $k {\mathrm{cm}}^2$, find $k$.

Find the area of a rhombus whose side is $6 \mathrm{cm}$ and whose altitude is $4.8 \mathrm{cm}$. If one of the diagonals is $8 \mathrm{cm}$ long and find the length of the other diagonal.

The floor of a building consists of $3000$ tiles which are rhombus shaped and each of its diagonals are $45 \mathrm{c}\mathrm{m}$ and $30 \mathrm{c}\mathrm{m}$ in length. If the total cost of polishing the floor is $\mathrm{₹}\mathrm{k}$ when the cost per ${\mathrm{m}}^2$ is $\mathrm{₹}4$, then find the value of $k$.

Mehraj wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is $10,500 {\mathrm{m}}^2$ and the perpendicular distance between the two parallel sides is $100 \mathrm{m}$, if the length of the side along the river is $k \mathrm{m}$, then find the value of $k$.

Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. If the area of the octagonal surface is $k {\mathrm{m}}^2$, find $k$.

There is a pentagonal shaped park as shown in the figure. For finding its area Asifa and Samina divided it in two different ways.

Find the area of this park using both ways. 

Diagram of the adjacent picture frame has outer dimensions $=24 \mathrm{c}\mathrm{m}\times 28 \mathrm{c}\mathrm{m}$ and inner dimensions $16 \mathrm{c}\mathrm{m}\times 20 \mathrm{c}\mathrm{m}.$ Find the area of each section of the frame, if the width of each section is same.