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 = 4 meters, c = 5 meters

Accepted Answer

Hey, everyone here, we are asked to calculate the area of the triangle provided the following side lengths. We are also asked to express our results to two decimal places. Here we are given side length A which is 11 inches. We then have side length B which is 18 inches. And lastly, we are given side length, side length C which is 23 inches. Here we have four answer choice options, answer choice, A 93.65 inches squared. Answer B 27.88 inches squared. Answer C 20.37 inches squared and answer D 96.75 inches squared. So to calculate the area of the triangle, we first want to notice that we are given all of these side links for our triangle. So this tells us that we can use Heron's formula to calculate the area. And with Heron's formula, we recall this formula is that the area of our triangle is equal to the square root of S multiplied by S minus A multiplied by S minus B multiplied by S minus C. So with this formula here, we can see it includes this variable S Well, we need to recall this variable S since it has its own formula and this formula for S is that S is equal to A plus B plus C all divided by two. In here, we can notice that we have already all of the values given for A B and C. So we can go ahead and simply substitute these values into our formula for S and find the value. So substituting we have 11 plus plus 23 all divided by two. And now simplifying, we find that our value for S is 26 inches. So with this value for S, we now have all of our components for Huron's formula. So we can now apply this formula by substituting in all of our given values plus the value we found for S. So doing this, we have the area is equal to the square root of 26 multiplied by 26 minus 11, multiplied by 26 minus 18, multiplied by 26 minus 23. So now our next step is to just simplify the value underneath the square root. And so doing this multiplying all of these terms together, we see that the area so far is the square root of 9360. So now we just want to simplify the square root by first breaking up our value underneath the root into its largest perfect square. So the largest perfect square of 9360 is 144. So we can break up our value. So we have the square root of multiplied by 65. And so now we can simplify our square root here since we know that the square root of 144 is 12. So this tells us that our area is exactly multiplied by the square root of 65. And since we cannot simplify this value any further, we just want to plug it into our calculators to find the decimal approximation. And so we find that 12 multiplied by the square root of 65 is approximately 96.7470929. And as we recall, we were asked to express our result to two decimal places. So that just means we need to round this value to the nearest 100th place. And so rounding, we find that the area of our triangle is approximately 96. inches squared. And with this value, we are left with answer choice D where again the area is 96.75 inches 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 = 4 meters, c = 5 meters

Key Concepts

Triangle Area Formulas

Heron's Formula

Properties of Triangles

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