Question

Heron’s formula: Area 

Use the triangle pictured to calculate the following measurements. 


Perimeter: p = ?
answer ⇒ 30 units


Semiperimeter: s = ?
answer ⇒ 15 units


Area: A ≈?
answer ⇒ 39.7 square units

Answer 1

Triangle is attached below

The triangle is 12 by 10 by 8

Perimeter:

To find perimeter we add all the sides of the triangle

Perimeter P = 12 + 10 + 8 = 30 units

Semi perimeter:

Semi perimeter is half of its perimeter

We know P = 30

Semi perimeter s=
`(p)/(2)` =
`(30)/(2)` = 15 units

Area:

If we know the sides of the triangle then we use Heron's formula to find the area of the triangle

`A = √(s(s-a)(s-b)(s-c))`

Where s= semi perimeter

a,b,c are the sides of the triangle

s= 15 units

a= 12 units

b= 10 units

c= 8 units

`A = √(15(15-12)(15-10)(15-8))`

`A= √(15(3)(5)(7))`

`A= √(15 * 105)`

`A= √(1575)`

A= 39.7 square units