Mensuration of Triangles
Formulas:
Right Triangle

altitude

base hypotenuse – it is always the longest side of a right tringle.
Side
Pythagorean Theorem
If the length of both a and b are known, then c can be calculated as follows. c=√(a^2+b^2 )
If the length of hypotenuse c and one leg (a or b) are known, then the length of the other leg can be calculated with the following equations: a=√(a^2+b^2 ) or b=√(a^2+b^2 )
Perimeter
Formula:
P=a+b+c
Area
Formula:
A= ½ bh or ½ ab or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3)

Example: a= 4 b= 3 c= ?

c=√42+√32 c=√16+9 c=√25 c=5 Perimeter
Formula:
P=a+b+c
P=4+3+5
P=12
Area
Formula:
A=1/2 bh or ½ ab or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3)
A=1/2 (3)(4)
=12/2
= 6cm2

Isosceles Triangle
P=s1+s2+s3
A=b√4a 2+√b2 / 4 or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3)

Line AB =5in Line AC=5in Line BC= ?
BC=?
AB=AC>BC
5+5>BC
10>BC
The base should be lesser then the sum of the legs so let the length BC = 9.
P=5+5+9
=19inches
A= b√4a 2+√b2 / 4 =9√4(9)2 – 52 / 4 =9√324-25 / 4 =9√299 / 4

Equilateral/ Equiangular Triangle
P=3s or a + b + c
A=s2√3 / 4 or The Heron’s Formula which is A= √p/2 (p/2-s1) (p/2-s2) (p/2-s3)

2 2

2
P=s1+s2+s3
=6cm
A=√3(1)(1)(1) A=s2√3 / 4 =√3 cm2 =22√3 /4 =4√3 / 4 =√3 cm2 Scalene Triangle
P=s1+s2+s3
A=Hero’s Formula = √p/2 (p/2-s1) (p/2-s2) (p/2-s3)

3 5

6
P=s1+s2+s3
=3+5+6 =14 cm
A=√p/2 (p/2-s1) (p/2-s2) (p/2-s3) =√7(7-3)(7-5)(7-6) =√7(4)(2)(1) =√56 =4√14 cm2