## Area formula for algebra

**Introduction :**

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, Together with geometry, analysis, topology, combinatory, and number theory, algebra is one of the main branches of pure mathematics. (Source – Wikipedia). The amount of space occupied by the closed figure is its area. This article deals with the algebra formulas for area and example problems using those formula.

Area formula for algebra:

Here are the algebraic formulas for area of shapes,

Area of square = a2 (a= side)

Area of Rectangle = length *width

The Area of a Circle = πr2. (r = radius and π=3.14

Area of parallelogram = b*h. {b is base and h is the height.}

Area of triangle = `1/2` (b*h). {b is base and h is the height}

Area of Rhombus = `1/2(` (x*y). {x and y are lengths of the diagonals }

Area of trapezoid= h* (`(b1+b2)/2)` {b1, b2= bases, h= altitude/height}

**Area formula for 3D shapes:**

Area of general prism = 2B + Ph {B=base, P= perimeter, h= height}

Area of triangular prism = ad + (a +b + c) h {a,b,c = sides and h=height , d = height of the base triangle}

Area of rectangular prism = 2lw + 2lh + 2wh {l=length, w=width, h=height}

Area of Regular square prism = 2(s2) + (4s) h {s=side, h=height}

Area of Regular pentagonal prism = 5as + 5sh {a=apothem, s=side, h=height}

Area of Regular hexagonal prism = 6as + 6sh {a=apothem, s=side, h=height}

Area of cube = 6a2 {a=side}

Area of regular triangular pyramid= `1/2` as + `3/2` s

*l*{l = slant height, a= altitude, s=side}

Area of regular square pyramid = s2 + 2sl {s=side, l = slant height}

Area of regular pentagonal pyramid = `5/2` as + `5/2` sl {a=apothem, l=slant height, s=side}

Area of regular hexagonal pyramid = 3as+asl {a=apothem, l=slant height, s=side}

Area of cylinder = 2(p r2) + 2prh { r=radius , h=height, p= 3.14}

Area of cone = prs+pr2 ( s=side, r=radius)

Area of sphere = 4pr2

Example algebra Problems:

**1) A triangle has the base of 6cm and height of 4cm. Calculate its area.**

**Solution:**

Given,

Base = b= 6cm,

Height = h= 4cm

By formula,

Area of triangle = `1/2` (b*h)

= ½( 6 *4)

= 12 cm2

**2) A sphere has the radius 12cm. What will be its area?**

**Solution:**

Radius = r = 12cm

By formula,

Area of sphere = 4pr2

= 4 * 3.14*122

= 1808.64cm2