Question

Daily life problems based on sum of n terms. Problems based on area of triangle

heron's formulae​

Answer 1

Step-by-step explanation:

Heron’s Formula, named after Hero of Alexandria 2000 years ago, can be used to find the area of a triangle given the three side lengths. The formula requires the semi-perimeter,

s

, or

12(a+b+c)

, where

a,b

and

c

are the lengths of the sides of the triangle.

Heron’s Formula: Area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

Let's use Heron’s formula to find the area of a triangle with side lengths 13 cm, 16 cm and 23 cm.

First, find the semi-perimeter or

s

:

s=12(13+16+23)=26

. Next, substitute our values into the formula as shown and evaluate:

A=26(26−13)(26−16)(26−23)−−−−−−−−−−−−−−−−−−−−−−−−√=26(13)(10)(3)−−−−−−−−−−−√=10140−−−−−√≈101 cm2

Now, let's answer the following questions.

Alena is planning a garden in her yard. She is using three pieces of wood as a border. If the pieces of wood have lengths 4 ft, 6ft and 3 ft, what is the area of her garden?

The garden will be triangular with side lengths 4 ft, 6 ft and 3 ft. Find the semi-perimeter and then use Heron’s formula to find the area.

sA=12(4+6+3)=132=132(132−4)(132−6)(132−3)−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=132(52)(12)(72)−−−−−−−−−−−−−−−−√=45516−−−−√≈28 ft2