In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square yards, of ΔABC.

The area of ΔABC is 6√6 sq. yards.

Step-by-step explanation:

The area of a triangle using the Heron's formula is:

Here s is given as follows:

The sides of the triangle ABC are as follows:

AB = 6 yd

BC = 7 yd

CA = 5 yd

Compute the value of s as follows:

Compute the area of ΔABC as follows:

Thus, the area of ΔABC is 6√6 sq. yards.

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)