In Exercises 13–16, find the area of the triangle having the give...

Question

In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit.a = 2 meters, b = 2 meters, c = 2 meters

Accepted Answer

Hey, everyone. Here we are asked to calculate the area of the triangle provided the following side links. Here we are given side links A B and C all with the same length of 19 ft. We are also asked to express the result to two decimal places. Here we have four answer choice options. Answer choice A 297.58 ft squared. Answer B 1768.53 ft squared. Answer C 156. ft squared and answer D 127.63 ft squared. So to begin this problem, we first want to notice that we have been given all of these side links for our triangle. So that means in order to calculate the area, we need to recall Huron's formula. Huron's formula states that the area is equal to the square root of S multiplied by S minus a multiplied by S minus B multiplied by S minus C. So now we can notice this variable S that appears in Huron's formula and that variable S has its own formula as we can recall. And this formula is that S is equal to A plus B plus C all divided by two. And so now we know that we have all of the values for A B and C. So we can simply substitute them into the formula for S and solve for S. So we have 19 plus plus 19 all divided by two. And now just simplifying, we get that S is equal to 28.5 ft. So now we have our value for S and we were already given the values for A B and C. So we can go ahead and apply Huron's formula by simply substituting in all of these values. So we have the square root of 28.5 five, multiplied by 28.5 minus 19, multiplied by 28.5 minus 19 and again, multiplied by 28.5 minus 19. So now we can just take this value here and plug it into our calculators to find the decimal approximation. And so we find that our area is approximately 156. then 3831. And so as we recall from our problem statement, we know we need to express the result to two decimal places. So that just means we need to round to the nearest hundreds. So our area approximately is 156.32 ft squared. And so with our final calculated calculated area for our triangle. We are left with answer choice C where again our area is 156.32 beat squared. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit.a = 2 meters, b = 2 meters, c = 2 meters

Key Concepts

Triangle Area Formulas

Heron's Formula

Equilateral Triangle Properties

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