NCERT Solutions for Chapter: Perimeter and Area, Exercise 1: Exercise

The side of a square garden is $150 \mathrm{m}$. A circular path of width $1.5 \mathrm{m}$ is laid inside the garden touching all the sides. Find the cost of laying the path at $\mathrm{Rs}. 28 \mathrm{per} {\mathrm{m}}^2$.

A circle of radius $7 \mathrm{cm}$ rotates inside and around the circumference of another circle. The smaller circle takes $10$ rotations to complete the circumference of the bigger circle. Find the radius of the bigger circle.

The side of a square metal sheet is $14 \mathrm{cm}$. A circular sheet of the greatest diameter is cut out from it and removed. Find the area of the remaining metal sheet.
The following steps are involved in solving the above problem. Arrange them in sequential order.
$\left(A\right)$ Area of circular sheet $=\pi r^2=\frac{22}{7}\times 7\times 7=154 {\mathrm{cm}}^2$
Area of square metal sheet $=(\text{ side }{)}^2=(14{)}^2=196 {\mathrm{cm}}^2$
$\left(B\right)$ Since the circular sheet has greatest diameter, diameter of the circle $=$ side of the square $=14 \mathrm{cm}$.
$\left(C\right)$ $\therefore$ Radius of the circular sheet $=\frac{14}{2}=7 \mathrm{cm}$
$\left(D\right)$ $\therefore$ The area of the remaining metal sheet $=$ Area of the square metal sheet $-$ Area of the circular sheet $=196-154=42 {\mathrm{cm}}^2$.

In the figure given below, $ABCD$ is a rectangle. $\mathrm{ED}=16 \mathrm{cm}, \mathrm{BF}=20 \mathrm{cm}, \mathrm{FG}=\mathrm{FC}=8 \mathrm{cm}$, and $\mathrm{FG}$ is perpendicular to $\mathrm{BC}$. If $\mathrm{CD}$ is half of $\mathrm{AD}$ then find the area of the shaded region. (in ${\mathrm{cm}}^2$)

In the figure given below, $ABCD$ is a quadrilateral and $BPDQ$ is a parallelogram. $AR=50 \mathrm{cm}, \mathrm{CQ}=70 \mathrm{cm}, \mathrm{BR}=60 \mathrm{cm}$, and $PR=40 \mathrm{cm}$. If the area of the quadrilateral $ABCD$ is $15,600 {\mathrm{cm}}^2$, then find the area of the parallelogram $BPDQ$ (in ${\mathrm{cm}}^2$).

Select the correct answer from the given options:

Using the information given in the figure, find the area of plot $PQRST$.

Find the area of a parallelogram-shaped shaded region. Also find the area of each triangle. What is the ratio of the area of shaded portion to the remaining area of the rectangle?