AREA OF POLYGONS

A polygon is a plane shape with straight sides. The area of a polygon measures the size of the region enclosed by the polygon. It is measured in units squared.

Area of Equilateral Triangle

A triangle with all three sides of equal length. All the angles are 60°.

Formula for area of an equilateral triangle :

= (√3/4)a²

Area of Scalene Triangle

A scalene triangle is a triangle that has three unequal sides.

Formula for area of a scalene triangle :

= √s(s - a)(s - b)(s - c)

where s = (a + b + c)/2.

Area of Square

A plane figure with four equal straight sides and four right angles.

Formula for area of a square :

= s² 

Area of Rectangle

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Formula for area of a rectangle :

= length x width

or

= l x w

Area of Parallelogram

A parallelogram is a quadrilateral with opposite sides parallel.

Formula for area of a parallelogram :

= base x height

or

= b x h

Area of Rhombus

A rhombus is a parallelogram with four equal sides and equal opposite angles.

Formula for area of a rhombus :

= (1/2) x (d₁ x d₂)

Area of Quadrilateral

A shape which is having four sides is generally called quadrilateral.

Formula for area of a quadrilateral :

= (1/2) x d x (h₁ + h₂)

Area of Trapezoid

A quadrilateral with one pair of sides parallel.

Formula for area of a trapezoid :

= (1/2) x h(a + b)

Example 1 :

Find the area of the parallelogram.

Solution :

Area of the parallelogram = b x h

Substitute b = 14 and h = 6.

  = 14 x 6

= 84 cm²

Example 2 :

What is the area of a parallelogram that has a base of 12.75 in. and a height of 2.5 in.?

Solution :

Area of the parallelogram = b x h

Substitute b = 12.75 and h = 2.5.

= 12.75 x 2.5

= 31.875 in²

Example 3 :

Find the area of trapezoid.

Solution :

Area of the trapezoid = (1/2) x h(a + b)

Substitute a = 42, b = 36 and h = 24.

  = (1/2) x 24(36 + 42)

= 12 x 78

= 936 in²

Example 4 :

The bases of a trapezoid are 11 meters and 14 meters. If its height is 10 meters, find the area.

Solution :

Area of the trapezoid = (1/2) x h(a + b)

Substitute a = 11, b = 14 and h = 10.

= (1/2) x 10(11 + 14)

= 5 x 25

  = 125 m²

Example 5 :

The diagonals of a rhombus are 21 m and 32 m. What is the area of the rhombus?

Solution :

Area of rhombus = (1/2) x (d₁ x d₂)

Subtract d₁ = 21 and d₂ = 32.

= (1/2) x (21 x 32)

= 21 x 16

= 336 m²

Example 6 :

Find the area of the given figure. Explain how you found your answer.

Solution :

In the given figure we can find two shapes, trapezoid and rectangle.

ABCD  is a trapezoid, DCEF is a rectangle.

Area of the given figure :

 =  Area of trapezoid + Area of rectangle

Area of trapezoid :

= (1/2) x h(a + b)

Substitute a = 10, b = 18 and h = 6

= (1/2) x 6(10 + 18)

= 3 x 28

= 84 ft²

Area of rectangle DCEF :

= l x w

Substitute l = 18 and w = 12.

= 18 x 12

= 216 ft²

Area of the given figure :

= 84 + 216

= 300 ft²

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