Use this formula, which is attributed to Heron of Alexandria but can be traced back to Archimedes.
Area = sqrt[s(s-a)(s-b)(s-c)],
where s=(a+b+c)/2 or perimeter/2.
find the area of each triangle to the nearest tenth.
in triangle YZX x=12cm z=16cm measure of angle Y= 130 degrees
in trianglE XYZ z= 11in. x= 7in. y= 13in.
2 answers
To use that formula on the first triangle, you need to figure the length of side y
Draw the altitude h from Y to XZ, meeting XZ at P
Let angle a = <XYP
h/16 = cos a
h/12 = cos(130-a)
16cos z = 12cos(130-a)
a = 68.81°
So, side y = XZ = 16sin68.81° + 12sin61.19° = 25.432
Now you can use Heron's formula to find the area: 73.54
Draw the altitude h from Y to XZ, meeting XZ at P
Let angle a = <XYP
h/16 = cos a
h/12 = cos(130-a)
16cos z = 12cos(130-a)
a = 68.81°
So, side y = XZ = 16sin68.81° + 12sin61.19° = 25.432
Now you can use Heron's formula to find the area: 73.54
1 answer