Question

Find the are of a triangle (picture provided)

Answer 1

Answer:

Choice b is correct.

Step-by-step 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

Answer:

B

Step-by-step explanation:

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

$A=\sqrt{p(p-a)(p-b)(p-c)},$

where a, b, c are lengths of triangle's sides and $p=\dfrac{a+b+c}{2}.$

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

$p=\dfrac{11.5+13.7+12.2}{2}=18.7.$

Hence,

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