**Surface area of pyramid with square base :**

Pyramid is basically a 3D shape. Even though we have formulas to find surface area of pyramid with square base, the basic idea of finding surface is to add the areas of all the faces.

To understand how to find surface area of a pyramid with square base, let us consider the pyramid given below.

Here is the basic idea to find surface area of the above pyramid.

**Surface Area = Sum of areas of all five faces (Including the base)**

For any pyramid, if the shape of the base is square, then we will have four side walls. The shape of each side wall will be a triangle with equal area.

In the above pyramid, the base is a square with side length "a" and each wall is a triangle with base "a" and height "h"

Let us find the area of each face separately.

Area of the base = a x a = a²

Area of each side wall = (1/2)ah

Area of all four side walls = 4 x (1/2)ah = 2ah

**Surface area of the above pyramid = a² + 2ah **

This is the formula to find surface area of a pyramid with square base.

We can apply the above explained basic idea to find surface area of a pyramid with triangular base.

Let us find surface area of a pyramid with triangular base.

For any pyramid, if the shape of the base is equilateral triangle, then we will have three side walls. The shape of each side wall will be a triangle with equal area.

In the above pyramid, the base is an equilateral triangle with side length "a".

And each wall is a triangle with base "a" and height "h"

Let us find the area of each face separately.

Area of the base = (√3/4)a²

Area of each side wall = (1/2)ah

Area of all 3 side walls = 3 x (1/2)ah = (3/2)ah

**Surface area of the above pyramid = ****(√3/4)a²**** + (3/2)ah **

This is the formula to find surface area of a pyramid with equilateral triangle base.

Note : If the base is not equilateral triangle and it is either scalene triangle or isosceles triangle, then the area of side walls will not be equal. We have to find area of each side wall separately.

**Problem : **

Find the surface area of the pyramid given below.

**Solution : **

**Surface area of the pyramid = Sum of areas of all 5 faces**

In the above pyramid, the base is a square with side length 5 cm and each wall is a triangle with base 5 cm and height 8 cm.

Let us find the area of each face separately.

Area of the base = 5 x 5 = 25 sq.cm

Area of each side wall = (1/2) x 5 x 8 = 20 sq.cm

Area of all 4 side walls = 4 x 20 = 80 sq.cm

Surface area of the above pyramid = 25 + 80

**Surface area of the above pyramid = 105 sq.cm**

**Problem 1 : **

Find the surface area of the pyramid given below.

**Solution : **

**Surface area of the pyramid = Sum of areas of all 4 faces**

In the above pyramid, the base is an equilateral triangle with side length 4 cm and each wall is a triangle with base 4 cm and height 6 cm.

Let us find the area of each face separately.

Area of the base = (√3/4) x 4² = 4√3 sq.cm

Area of each side wall = (1/2) x 4 x 6 = 12 sq.cm

Area of all 3 side walls = 3 x 12 = 36 sq.cm

Surface area of the above pyramid = (4√3 + 36) sq.cm

**Surface area of the above pyramid = 4(√3 + 9) sq.cm**

**Problem 2 : **

Find the surface area of the pyramid given below.

**Solution : **

**Surface area of the pyramid = Sum of areas of all 4 faces**

In the above pyramid, the base is an equilateral triangle with side length 4 cm and each wall is a triangle with base 4 cm and height 6 cm.

Let us find the area of each face separately.

Area of the base = (√3/4) x 6² = 9√3 sq.cm

Area of each side wall = (1/2) x 6 x 10 = 30 sq.cm

Area of all 3 side walls = 3 x 30 = 90 sq.cm

Surface area of the above pyramid = (9√3 + 90) sq.cm

**Surface area of the above pyramid = 9(√3 + 10) sq.cm**

After having gone through the stuff given above, we hope that the students would have understood "Surface area of pyramid with square base".

Apart from the stuff given above, if you want to know more about "Surface area of pyramid with square base", please click here

Apart from the stuff, "Surface area of pyramid with square base", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**