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. 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. 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). 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 = $\frac{\text{1}}{\text{2}}$ × bh. 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). 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. 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. 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). 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 = $\frac{\text{1}}{\text{2}}$ × bh. 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). 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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