Find the area of each triangle ABC.

a = 76.3...

Question

Find the area of each triangle ABC.

a = 76.3 ft, b = 109 ft, c = 98.8 ft

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the area of the triangle. Pqr where side P is 88.4 centimeters. Q is 123 centimeters and R is 64.8 centimeters. For our answer choices. A says the area is 1738 square centimeters. B 1378 square centimeters. C 3756 square centimeters and D 2756 square centimeters. Now, before we try to figure out the area, let's try to sketch or triangle here to figure out what's going on. So a triangle would probably look something like this. OK? Where side P will be equal to 88.4 centimeters. Side Q equals 123 centimeters and side R equals 64.8 centimeters. OK. So this would be our triangle P. Sorry, let me put them in here. PQ R. Now, let's think about it. Do we know anything that can help us to find the area of a triangle if we don't know its perpendicular height? Well, we can recall Heron's formula and recall that by Heron's formula. OK. It tells us the area of our triangle is going to be equal to the square root of S where S represents the semi perimeter of the triangle multiplied by, in this case, S minus P multiplied by S minus Q multiplied by SS minus R. So this will be the area for a triangle. OK. Where the semi perimeter is really just half of the parameter of the triangle. So the semi parameter is going to be P plus Q plus R divided by two. So if we can find the semi perimeter, we can plug it into our formula to solve for the area of our triangle. So let's try to figure that out. Now let's plug the values of PQ and R into our formula for the semi perimeter. So that means the semi parameter is going to be P 88.4 plus Q 123 plus R 64.8 all divided by two. Now when we add those up, our numerator will be equal to 276.2 and 276.2 divided by two equals 138.1. So the semi perimeter of our triangle is 138.1 centimeter centimeters. Sorry. Now that we have the value of XS, we can solve a, our area. So solving for a by plugging it into a formula, plugging s into our formula A is going to be equal to the square root. I'll try to draw this as long as I can, but it's gonna be the square root of S 138.1 multiplied by S minus P. So that's 138.1 minus uh 88.4 multiplied by S minus Q 138.1 minus 123 multiplied by S minus R 138.1 minus 64.8. Now that we have that we can try to simplify what's under our square root when we do that. OK? To know we'll have the square root of 138.1 multiplied by 49.7. OK? Because that is what is gonna be 138.1 minus 88.4 multiplied by 15.1 138 minus 123 multiplied by 73.3 138.1 minus 64.8. So we're finding the square root of this product. Let's go ahead and put this product into our calculator. No, I mean, you can expect to get a very big number and we do get the value under the square root to be equal to 7,596,805 0.183. So the area of our triangle is the square root of that value. Now, when we find the square root of that value, we get our area to be equal to 2756.230249 square centimeters. Now, remember all of our answers were rounded to the nearest square centimeter. So when we do that, we get our area to be approximately equal to 2756 square centimeters. That's the area of triangle P QR. And if we look back in our answer choices, that would be choice. D thanks a lot for watching everyone. I hope this video helped.

Find the area of each triangle ABC.

a = 76.3 ft, b = 109 ft, c = 98.8 ft

Key Concepts

Triangle Area Formula

Semi-Perimeter

Heron's Formula

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