Question

Heron’s formula: Area Use the triangle pictured to calculate the following measurements. Perimeter: p = units Semiperimeter: s = units Area: A ≈ square units

Answer 1

p= 30 units

s= 15 units

a=39.7 square units

Answer 2

the complete question is

Heron’s formula: Area Use the triangle pictured to calculate the following measurements. Perimeter: p = units Semiperimeter: s = units Area: A ≈ square units. The triangle is 8 by 12 by 10

Part a) Calculate the Perimeter:

 The perimeter of the triangle is the sum of its sides.

$P = 8 + 12 + 10\\ P=30 units$

the answer Part a) is

The perimeter is equal to $30 units$

Part b) Calculate the Semi-perimeter: 

The semiperimeter of a polygon is half its perimeter.

 $s = P / 2\\ s=30/2\\ s=15 units$

 the answer part b) is

the semiperimeter is equal to $15 units$

Part c) Calculate the Area

we know that

You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that
It is called "Heron's Formula"

 $A = \sqrt{(s * (s-a) * (s-b) * (s-c))}$

 where

 s: is the semi-perimeter

 a, b, c are the length sides.

$s=15 units\\ a=8 units\\ b=12 units\\ c=10 units$

$A = \sqrt{(15 * (15-8) * (15-12) * (15-10))}$

$A = \sqrt{(15 * (7) * (3) * (5))}$

$A = \sqrt{(15 * (105) )}$

$A = \sqrt{(1,575 )}$

$A= 39.7 units^{2}$

the answer Part c) is

$A= 39.7 units^{2}$