Perimeter and Area of Figures: Suppose you are planning to construct a new house, and you want to put the fence around the property. The most important thing you need to know is perimeter. But what does perimeter mean? Let us find an answer to this in the article below. Let us study the topic Perimeter and area of figures in detail.
Perimeter and Area of Figures
The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence. If the yard is 50 ft × 50 ft your fence is 200 ft long. Area and perimeter are very important terms which can be applied to any shape of the figure.
The area is a measure of the space contained within an object. In the same yard, an area is a measure you need to be to start a lawn. The area has units of distance squared. For a 50 ft × 50 ft you need 50 × 50 = 2500 sq feet of grass. So let us find out the area and perimeter of the figures like rectangle and square.
What is Area?
The area is the amount of two-dimensional space taken up by the object. It is measured in square units.
Area of the rectangle = length × width
Area of the Square = s², where ‘s’ = side length of the square
A perimeter is the total boundary of the two-dimensional shape. If you want to provide a fencing around the entire field you need its perimeter. Suppose you want to lay a pathway inside the field to keep a watch on your field you need its perimeter. The units of the perimeter are, cm, m etc.
Perimeter of Rectangle
We can see that in the rectangle the two sides are parallel and equal and also all the angles are 90 degrees. The perimeter of the rectangle is the distance around the outside of the rectangle.
P = l+ b+ l+ b (where l is the length and b is the breadth of the rectangle)
= 2l + 2b
P = 2 ( l + b )
Let us take an example of a book. The length of the book is 15 cm and breadth is 25 cm. So to find the perimeter of the book = length + breadth = 15+ 25 = 40 cm. Now, perimeter = 2 ( l +b ) = 2 ( 40 ) = 80 cm.
Perimeter of Square
A rectangle with all its sides equal is a square. So, a perimeter of a square = side + side + side + side. Hence, the perimeter of a square with side S is given by
P =4 × S
Let us take an example of a tile. The length of the tile is 10 cm each. The perimeter of tile = 4 × 10 cm = 40 cm.
Comparing Perimeters of Rectangles and Squares from Their Shapes
Suppose the size of the square is 5 cm and the size of the rectangle is 5 × 4 cm. The side of a square is equal to the length of the rectangle.
- So perimeter of a square is = 5 × 4 = 20 cm
- So perimeter of a rectangle is 2 ( 5 + 4 ) = 18 cm
Therefore the Perimeter of the square is greater than that of the rectangle.
Solved Examples for You
Question 1: The total boundary length of a closed figure is called
Answer : C is the correct option. The total boundary length of a closed figure is called the perimeter.
Question 2: Area is ____
- 1- Dimensional
- 2- Dimensional
- 3- Dimensional
- 4- Dimensional
Answer : B is the correct option. The area is 2- Dimensional. Because it has length and width.
Question 3: What is a plane figure?
Answer: It refers to a flat 2D (two-dimensional) shape. In addition, they can be made of straight lines, curved lines, or both curved and straight lines. Furthermore, plane figures such as square and rectangle have length and breadth but other plane figures don’t have length and breadth.
Question 4: What are geometric figures?
Answer: These are the figures that we see in math, and they have a different name. Such as circle, trapezium, triangle, square, rectangle, heart, diamond, etc. are some of the geometric shapes. However, some of the shapes such as polygons have been described based on their number of sides.
Question 5: Are cones and cylinders a plane figure?
Answer: No, the cone is a solid three-dimensional figure that has a circular base and one vertex. Besides, a cylinder is a solid figure with two parallel congruent bases. However, a plane figure is flat two-dimensional figures or shapes.
Question 6: State the name of 15 basic shapes?
Answer: Basic shapes refer to all those plane figures that we can draw on a piece of paper. Besides, the 15 basic shapes are rectangle, square, circle, triangle, heptagon, hexagon, pentagon, octagon, nonagon, decagon, parallelogram, kite, trapezium, rhombus, and quadrilateral.