Question

Find the are of a triangle (picture provided)

Answer 1

Choice b is correct.

Explanation:

We have given the sides of triangle.

a = 11.5, b = 13.7 and c = 12.2

We have to find the area of the triangle.

The formula to find the area of the triangle when three sides are given is:

A = √p(p-a)(p-b)(p-c)

where p = (a+b+c) / 2

p = (11.5+13.5+12.2)/2

p = 18.7

A = √18.7(18.7-11.5)(18.7-13,7)(18.5-12.2)

A = 30√4.862 units²

A≈ 66.1 units²

Answer 2

B

Explanation:

Use the Heron's formula for the area of the triangle:

`A=√(p(p-a)(p-b)(p-c)),`

where a, b, c are lengths of triangle's sides and
`p=(a+b+c)/(2).`

Since
`a=11.5,\ b=13.7,\ c=12.2,` then

`p=(11.5+13.7+12.2)/(2)=18.7.`

Hence,

`A=√(18.7(18.7-11.5)(18.7-13.7)(18.7-12.2))=√(18.7\cdot 7.2\cdot 5\cdot 6.5)=\\ \\=√(11\cdot 1.7\cdot 9\cdot 4\cdot 0.2\cdot 5\cdot 5\cdot 1.3)=30√(11\cdot 1.7\cdot 0.2\cdot 1.3)=30√(4.862)\approx 66.1\ un^2.`