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Mensuration

Mensuration of Parallelograms

Area of a parallelogram: Recall that a parallelogram is a quadrilateral with both pairs of opposite sides parallel. Parallelograms come in the form of rectangles, rhombi and squares. When trying to determine the area of a parallelogram, it will be necessary to identify the base and the height of the parallelogram. The base of a parallelogram can be any side. The height of the parallelogram is the length of an altitude. The altitude of a parallelogram is a segment perpendicular to the base with endpoints on the base and the side opposite the base.

The area of a parallelogram is given by the product of the base and height. If a parallelogram has an area of 'A' square units, a base of 'b' units and a height of 'h' units, then A = bh.

Perimeter of a parallelogram: The perimeter of a parallelogram is the length of its boundary, which can be found by adding together the length of each side. Since each pair of opposite sides has the same length, the perimeter is twice the base length plus twice the side length or twice the sum of base length and side length.

If a parallelogram has a perimeter of 'P' units, a base of 'a' units and a side of 'b' units, then P = 2a + 2b or P = 2(a + b).

Mensuration of Rectangles

Area of a rectangle: A quadrilateral with four right angles is called a rectangle or A parallelogram each of whose angles measures 90° is called a rectangle. To find the area of a rectangle, multiply the length by the breadth. If a rectangle has an area of 'A' square units, a length of 'l' units and a breadth of 'b' units, then A = lb.

Perimeter of a rectangle: The perimeter of a rectangle is the length of its boundary, which can be found by adding together the length of each side. Since each pair of opposite sides has the same length, the perimeter is twice its width plus twice its breadth or twice the sum of width and breadth.

If a rectangle has a perimeter of 'P' units, a length of 'l' units and a breadth of 'b' units, then P = 2l + 2b or P = 2(l + b).

Mensuration of Squares

Area of a square: A square is a rectangle with four equal sides. To find the area of a square, multiply the length of one side by itself. If a square has an area of 'A' square units and length of a side 's' units, then A = s × s = s2.

Perimeter of a square: The perimeter of a square is the length of its boundary, which can be found by adding together the length of each side. Since all sides are equal in length, the perimeter is 4 times the length of a side.

If a square has a perimeter of 'P' units, and a side of length 's' units, then P = 4s.

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