Notes On Plane Figures - CBSE Class 7 Maths

Perimeter of a closed figure is the distance around it, whereas area is the region enclosed by closed figure.
Perimeter of a regular polygon = number of sides x length of one side.

Area and perimeter of a rectangle
The perimeter of a rectangle is twice the sum of the lengths of its adjacent sides.
Perimeter of a rectangle of length 'l' units and breadth 'b' units = 2(l + b).
The area of a rectangle is the product of its length and breadth.
Area of a rectangle of length 'l' units and breadth 'b' units = l × b.
The perimeter of rectangle ABCD = 2(AB + BC).
Area of rectangle ABCD = AB x BC.

rectangle, quadrilateral, perimeter of a rectangle, area of a rectangle

Each diagonal of a rectangle divides it into two triangles that are equal in area.

Area and perimeter of a square
The perimeter of a square with side s units is the four times the length of its side.
Perimeter of a square with side s units = 4 × s
The area of a square with side s is is equal to side multiplied by side.
Area of a square with side s units = s × s

The perimeter of square ABCD = 4AB or 4BC or 4CD or 4DA.
Area of square ABCD = AB2 or BC2 or CD2 or DA2.

square, quadrilateral, perimeter of a square, area of a square

The diagonals of a square divide it into four triangles that are equal in area. A rectangle and a square having the same perimeter need not have the same area. If the perimeter of a figure increases it is not necessary that its area also increases.

Area and perimeter of a triangle
The perimeter of a triangle is the sum of the lengths of its sides.
Perimeter of a triangle with sides a, b and c = (a + b + c).

perimeter of a triangle, lengths of sides of a triangle

The area of a triangle is the space enclosed by its three sides.
Area of a triangle is half of the product of its base and the corresponding altitude.
Area of a triangle with b as the base and h as the altitude = 1 2  × bh.


area of a triangle, space enclosed by its three sides

Triangles equal in area need not be congruent, but all congruent triangles are equal in area.

Area and perimeter of a parallelogram
The perimeter of a parallelogram is twice the sum of the lengths of the adjacent sides.
The area of a parallelogram is the product of its base and the corresponding altitude.

Area of a parallelogram with b as the base and h as the altitude = b × h.
Any side of a parallelogram can be considered as the base. The perpendicular drawn on that side from the opposite vertex is known as the height (altitude).

The perimeter of parallelogram ABCD = 2(AB + BC)
Area of parallelogram ABCD = (AB x DE) or (AD x BF).

quadrilateral, perimeter of a parallelogram, area of a parallelogram perpendicular height, base, altitude

A parallelogram in which the adjacent sides are equal is called a rhombus.

The perimeter and area of a rhombus can be calculated using the same formulae as that for a parallelogram.



Conversion of units

1cm = 10 mm
1 cm2 = 100 mm2
1 m2 = 10000 cm2
1 hectare = 10,000 m2

Summary

Perimeter of a closed figure is the distance around it, whereas area is the region enclosed by closed figure.
Perimeter of a regular polygon = number of sides x length of one side.

Area and perimeter of a rectangle
The perimeter of a rectangle is twice the sum of the lengths of its adjacent sides.
Perimeter of a rectangle of length 'l' units and breadth 'b' units = 2(l + b).
The area of a rectangle is the product of its length and breadth.
Area of a rectangle of length 'l' units and breadth 'b' units = l × b.
The perimeter of rectangle ABCD = 2(AB + BC).
Area of rectangle ABCD = AB x BC.

rectangle, quadrilateral, perimeter of a rectangle, area of a rectangle

Each diagonal of a rectangle divides it into two triangles that are equal in area.

Area and perimeter of a square
The perimeter of a square with side s units is the four times the length of its side.
Perimeter of a square with side s units = 4 × s
The area of a square with side s is is equal to side multiplied by side.
Area of a square with side s units = s × s

The perimeter of square ABCD = 4AB or 4BC or 4CD or 4DA.
Area of square ABCD = AB2 or BC2 or CD2 or DA2.

square, quadrilateral, perimeter of a square, area of a square

The diagonals of a square divide it into four triangles that are equal in area. A rectangle and a square having the same perimeter need not have the same area. If the perimeter of a figure increases it is not necessary that its area also increases.

Area and perimeter of a triangle
The perimeter of a triangle is the sum of the lengths of its sides.
Perimeter of a triangle with sides a, b and c = (a + b + c).

perimeter of a triangle, lengths of sides of a triangle

The area of a triangle is the space enclosed by its three sides.
Area of a triangle is half of the product of its base and the corresponding altitude.
Area of a triangle with b as the base and h as the altitude = 1 2  × bh.


area of a triangle, space enclosed by its three sides

Triangles equal in area need not be congruent, but all congruent triangles are equal in area.

Area and perimeter of a parallelogram
The perimeter of a parallelogram is twice the sum of the lengths of the adjacent sides.
The area of a parallelogram is the product of its base and the corresponding altitude.

Area of a parallelogram with b as the base and h as the altitude = b × h.
Any side of a parallelogram can be considered as the base. The perpendicular drawn on that side from the opposite vertex is known as the height (altitude).

The perimeter of parallelogram ABCD = 2(AB + BC)
Area of parallelogram ABCD = (AB x DE) or (AD x BF).

quadrilateral, perimeter of a parallelogram, area of a parallelogram perpendicular height, base, altitude

A parallelogram in which the adjacent sides are equal is called a rhombus.

The perimeter and area of a rhombus can be calculated using the same formulae as that for a parallelogram.



Conversion of units

1cm = 10 mm
1 cm2 = 100 mm2
1 m2 = 10000 cm2
1 hectare = 10,000 m2

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