heron’s formula. heron’s formula is used to determine the area of any triangle when only the...
TRANSCRIPT
Heron’sFormula
Heron’s Formula is used to determine the area of any triangle when only the lengths of the three
sides are known.
2
cbas
where
c)b)(sa)(s(s)(sk
The ‘s’ represents the
semi-perimeter.
The semi-perimeter is nothing more
than half the perimeter.
2
cbas
Add the lengths of the three known
sides together and then divide by two.
Next substitute the known values into Heron’s Formula then solve for the
area.
A
B
C
a
b
c
Side a=5
Side b=8
Side c=7
First determine ‘s’, which is the
semi-perimeter.
2
cbas
2
785s
2
20s
10s
Now we know:
Side a: = 5
Side b: = 8
Side c: = 7
Semi-perimeter: s = 10
Replace the letters in Heron’s Formula with their respective known values. (Substitute)
c)b)(sa)(s(s)(sk
7)8)(105)(10(10)(10k
c)b)(sa)(s(s)(sk
(3)(10)(5)(2)k
7)8)(105)(10(10)(10k
c)b)(sa)(s(s)(sk
300k
(3)(10)(5)(2)k
7)8)(105)(10(10)(10k
c)b)(sa)(s(s)(sk
320508.17k
300k
(3)(10)(5)(2)k
7)8)(105)(10(10)(10k
c)b)(sa)(s(s)(sk
3.17k
320508.17k
300k
(3)(10)(5)(2)k
7)8)(105)(10(10)(10k
c)b)(sa)(s(s)(sk
Another problem solved via
trigonometry!
Try this one on your own!
Side a = 5
Side b = 6
Side c = 7
Did you getArea = k = 14.7
Now for the solution of this
problem.
First determine ‘s’, which is the
semi-perimeter.
2
cbas
2
765s
2
18s
9s
Now we know:
Side a: = 5
Side b: = 6
Side c: = 7
Semi-perimeter: s = 9
c)b)(sa)(s(s)(sk
7)6)(95)(9(9)(9k
c)b)(sa)(s(s)(sk
2)(9)(4)(3)(k
7)6)(95)(9(9)(9k
c)b)(sa)(s(s)(sk
216k
2)(9)(4)(3)(k
7)6)(95)(9(9)(9k
c)b)(sa)(s(s)(sk
696938.14k
216k
2)(9)(4)(3)(k
7)6)(95)(9(9)(9k
c)b)(sa)(s(s)(sk
7.14k
696938.14k
216k
2)(9)(4)(3)(k
7)6)(95)(9(9)(9k
c)b)(sa)(s(s)(sk
This was createdby
Frank J. Antoniazzi Jr.on
15 April 2002