# SURFACE AREA OF PYRAMID WITH TRIANGULAR BASE

## About "Surface area of pyramid with triangular base"

Surface area of pyramid with triangular base :

Pyramid is basically a 3D shape. Even though we have formulas to find surface area of pyramid with triangular 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 triangular 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 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.

## Surface area of pyramid - Practice problems

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

Let us look at the next problem on "surface area of pyramid"

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 triangular base".

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

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

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6