In Exercises 25–30, use Heron's formula to find the area of each ...

Question

In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit.

a = 4 feet, b = 4 feet, c = 2 feet

Accepted Answer

Hello everybody. I hope you are doing. All right. Today, today we're going to be looking at this question that states for the given triangle determine the area of the triangle using Huron's formula and report the area round into the nearest square unit. Now, they tell us the size of our triangle with side P equals 12 m, side Q equals 12 m and side R equals two m. Now, the answer choice provided are a 11 square meters, B 12 square meters C 13 square meters or D square meters. Now, the first thing we have to do with a question like this is ask ourselves, what is Huron's formula? So let's recall that. So he runs formula is a relatively simple formula that states that area is equal to the square root of S multiplied by open parentheses. S minus a closed parentheses, multiplied by open parentheses. S minus B closed parentheses multiplied by open parentheses. S minus C close parentheses where A B and C our sides and S is the semi perimeter. So they give us the values of all our sides, but they don't give us the value of the semi further. So that is something we have to solve for. And luckily, we have a formula for that. So the semi perimeter is just half of the perimeter. So we know that the perimeter is just adding up all the sides. So a semi perimeter would be, let's say A plus B plus C adding up all the sides. And that entire addition divided by two, that would be half of the perimeter. So we plug our sides in. We'll have s is equal to 12 plus 12 plus two, divided by two, which is equal to 26 divided by two, which is equal to 13. And just like that, we have our missing piece, the same perimeter and we can go ahead and plug into Huron's formula. So we'll have that area A is equal to the square root of 13, multiplied by open parentheses. 13 minus the first side which is 12 closed parentheses, multiplied by open parentheses. 13 minus the second side which was also 12 closed parentheses, multiplied by open parentheses. 13 minus the last side which was two and closed parentheses. And all of that will be within the square root. Now, we simplify the parentheses. We have that A is equal to the square roots of 13 multiplied by one multiplied by one multiplied by 11. And if we distribute all that, we'll have that A is equal to the square root of 43. And if we plug that into our calculator, we have that the area will be around 11.96 which will round out to 12 m squared or 12 squared meters. Which if we compare that to our choices, we see that it matches with a choice B. So we can see how a simple formula like Huron's formula can help us find the area of our triangle. So I hope that was helpful. And until next time.

In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit. a = 4 feet, b = 4 feet, c = 2 feet

Key Concepts

Heron's Formula

Semi-perimeter

Triangle Inequality Theorem

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