Question Video: Finding the Area of a Composite Figure Using Heron′s Formula Mathematics

Find the area of the figure below using Heron’s formula, giving the answer to three decimal places.

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Video Transcript

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.