# GMAT Quant: Geometry â€“ Area

Area is the space that is confined within any shape. There are many standard figures who has a fixed formula for calculating their areas, while some needs to be broken down to two or more shape so that their area can be calculated.

Letâ€™s check some standard formulas for some of the shapes:

Area of a Triangle

$Area = \frac{1}{2} \times b \times h$

Area of a Circle

$Area = \pi r^{2}$

Area of a Square

$Area = (side)^{2}$

Area of a Rectangle

$Area = Length \times Width$

Area of a Parallelogram

$Area = Base \times Height$

Also Read:Â GMAT Quant: Arithmetic â€“ Numbers

Area of Trapezoid

$Area = 5 \times (base_1 + base_2) \times height$

Area of a Rhombus

Rhombus is a shape whose all sides are equal but only opposite sides are parallel to one another. The diagonals of rhombus bisect at 90Â°.

$Area = 5 \times diagonal_1 \times diagonal_2$

Letâ€™s solve a question and see how easy calculating area is:

Question: A square of area 81 sq. units, made of a thin wire, is converted into semi-circle. What is the area of the semi-circle?

1. 49
2. 77
3. 154
4. 84
5. 98

Solution:

Perimeter of square = Perimeter of semi-circle Â Â Â Â (Equation 1)

$Area \; of \; square = a^2 = 81$

So, a = 9

Perimeter of square = 9 Ã— 4 = 36

From Equation 1,

$\pi r + 2 r = 36$ $\frac{22}{7} r + 2 r = 36$ $\frac{36 r}{7} = 36$

So, $r = 7$

Area of semi-circle =Â  $A = \frac{\pi r^2}{2}$

Area = $A = \frac{22}{7} \times 7 \times 7 \times \frac{1}{2} = 77 \; sq. \; units$

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