Video Transcript
𝐴𝐵𝐶 is a triangle, where 𝐵𝐶
equals 28 centimeters, 𝐴𝐶 equals 20 centimeters, and 𝐴𝐵 equals 24
centimeters. Find the area of 𝐴𝐵𝐶 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 𝑎, 𝑏, and 𝑐, then the
area of this triangle is equal to the square root of 𝑠 multiplied by 𝑠 minus 𝑎
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 𝑎 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.
