Question Video: Finding the Area of a Triangle given the Lengths of Its Three Sides | Nagwa Question Video: Finding the Area of a Triangle given the Lengths of Its Three Sides | Nagwa

Question Video: Finding the Area of a Triangle given the Lengths of Its Three Sides Mathematics • Second Year of Secondary School

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𝐴𝐡𝐢 is a triangle, where 𝐡𝐢 = 28 cm, 𝐴𝐢 = 20 cm, and 𝐴𝐡 = 24 cm. Find the area of 𝐴𝐡𝐢 giving the answer to the nearest square centimeter.

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Video Transcript

𝐴𝐡𝐢 is a triangle, where 𝐡𝐢 equals 28 centimeters, 𝐴𝐢 equals 20 centimeters, and 𝐴𝐡 equals 24 centimeters. Find the area of 𝐴𝐡𝐢 giving the answer to the nearest square centimeter.

So, the first thing we’ve done is just drawn a quick sketch to visualize what’s happening. So, what we have is a triangle. And in that triangle, we have three sides, and we know each of their lengths. So, therefore, if we know the lengths of each of the sides of our triangle and we want to find the area, then what we’re going to do is use Heron’s formula. Well, if we quickly remind ourselves of Heron’s formula, if we have a triangle lengths π‘Ž, 𝑏, and 𝑐, then the area of this triangle is equal to the square root of 𝑠 multiplied by 𝑠 minus π‘Ž multiplied by 𝑠 minus 𝑏 multiplied by 𝑠 minus 𝑐, where 𝑠 is the semiperimeter, so half of the perimeter of our triangle. And we could find that by adding together each of the sides, so π‘Ž plus 𝑏 plus 𝑐, and then dividing it by two.

So, the first thing we’re gonna do is find out 𝑠. And to find this, what we’re gonna do is add together the three side lengths, so 28 plus 20 plus 24, and then divide this by two. And this is gonna give us a semiperimeter of 36 centimeters. So, therefore, the area is gonna be equal to the square root of 36 multiplied by 36 minus 28 multiplied by 36 minus 20 multiplied by 36 minus 24, which is gonna be equal to the square root of 55296. Well, this is equal to 235.1510153. However, is this the final answer? Well, no because if we look back at the question, we can see that we want the answer to the nearest square centimeter. So, therefore, we can say that to the nearest square centimeter, the area of the triangle is 235 centimeters squared.

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