Find the area of the figure below
using Heron’s formula, giving the answer to three decimal places.
The first thing to do is to divide
this composite shape up into a triangle and a rectangle. The area of the rectangle is 64
times 55 equals 3520 square centimeters. We are going to work out the area
of the triangle using Heron’s formula, which gives us the area as the square root of
𝑠 times 𝑠 minus 𝑎 times 𝑠 minus 𝑏 times 𝑠 minus 𝑐, where 𝑎, 𝑏, and 𝑐 are
the lengths of the triangle′s sides and 𝑠 is its semiperimeter.
The semiperimeter of the triangle
is just half of its perimeter, or 58 plus 58 plus 55 divided by two. That’s 85.5. We can now substitute this value of
85.5 for 𝑠 and the lengths 58, 58, and 55 of the triangle’s sides into Heron’s
formula. A calculator is useful at this
point. We find that the area of the
triangle is 1404.319 square centimeters to three decimal places. Adding together the area of the
rectangle and the triangle, we find that the total area is 4924.319 square
centimeters to three decimal places.