Question

The following exercise uses Heron's formula One triangular plot has sides 5 yards, 6 yards, and 7 yards. Another has sides 3 yards, 6 yards, and 7 yards. Find the area of each plot. (Round your answers to one decimal place.) first plot second plat Which plot endloses the larger area? first plot second plat

Answer 1

`\text{Area of 1st plot}\approx 14.7\text{ yards}^2`

`\text{Area of 2nd plot}\approx 8.9\text{ yards}^2`

1st plot encloses the larger area.

Explanation:

We have been given the sides of two triangles. We are asked to find the area of given triangles using Heron's formula.

The area of a triangle with sides a, b and c would be:

`\text{Area of }\Delta =√(S(S-a)(S-b)(S-c))`, where S is the semi-perimeter of triangle.

`S=(5+6+7)/(2)=(18)/(2)=9`

Substitute given side lengths:

`\text{Area of 1st plot}=√(9(9-5)(9-6)(9-7))`

`\text{Area of 1st plot}=√(9(4)(3)(2))`

`\text{Area of 1st plot}=√(216)`

`\text{Area of 1st plot}=14.6969\approx 14.7`

Therefore, the area of 1st plot would be 14.7 square yards.

`S=(3+6+7)/(2)=(16)/(2)=8`

Substitute given side lengths:

`\text{Area of 2nd plot}=√(8(8-3)(8-6)(8-7))`

`\text{Area of 2nd plot}=√(8(5)(2)(1))`

`\text{Area of 2nd plot}=√(80)`

`\text{Area of 2nd plot}=8.9442\approx 8.9`

Therefore, the area of 2nd plot would be 8.9 square yards.

Since area of first plot is greater than 2nd plot, therefore, 1st plot encloses the larger area.