R. Gupta Solutions for Chapter: Area and Perimeter, Exercise 1: EXERCISE

If the length of a rectangle is increased by $20\%$, then by how much percent its breadth must be decreased so as to keep its area unaltered?

Each side of a given square is $5 \mathrm{cm}$, and assuming the two opposite sides of this square as diameters, two semicircles are drawn inside the square. If these semicircles are cut out from the square, then the area of the remaining portion of the given square will be _____.

If the area of a triangle, whose base is $6 \mathrm{cm}$, is equal to the area of a circle of radius $6 \mathrm{cm}$, then find the height of this triangle.

If the areas of two squares are in the ratio of $25:16$, then their perimeters will be in the ratio of _____.

The length and breadth of a room are in the ratio $2:1$. If the cost of cementing the floor at $₹0.75/{\mathrm{m}}^2$ comes to be $₹864$, and the cost of polishing the walls at $₹3.25/{\mathrm{m}}^2$ comes to be $₹884$, then the height of the room is _____.

A garden is $24 \mathrm{m}$ long and $14 \mathrm{m}$ wide. There is a $1 \mathrm{m}$ wide path outside the garden along its sides. If the path is to be constructed with square marble tiles $20 \mathrm{cm}\times 20 \mathrm{cm}$, find the number of tiles required to cover the path.

Two adjacent sides of a parallelogram are $40 \mathrm{m}$ and $30 \mathrm{m}$, respectively. If one diagonal of the parallelogram measures $50 \mathrm{m}$, find its area.

Four sides of a trapezium are $50 \mathrm{cm}, 17 \mathrm{cm}, 25 \mathrm{cm}$ and $12 \mathrm{cm}$, respectively. If the first of the four sides is parallel to the third, find the area of this trapezium.