### What's the Area? (Part II)

In the previous post, I promised to look at a few ways of determining the area of the following trapezoid. In this post, we'll look at the simplest answers, those offered by geometry.

We can easily break the trapezoid up into a rectangle and a triangle.

The area of the rectangle is 0.4 * 1.0 and the area of the triangle is 0.3 * 1.0 / 2. Add them together for a total of 0.55. Simple and straight forward.

MathWorld tells us that the formula for a right trapezoid is 1/2 * a * (h1 + h2), and 1/2 * 1.0 * (0.4 + 0.7) gives us the same result of 0.55.

With little effort, geometry offered us a couple of solutions to the problem.

The geometric solution.

Q: When should we use it?

A: IMHO, whenever we can.

Pros: Simple and straightforward.

Cons: None

Next, let's look to calculus for a solution.

We can easily break the trapezoid up into a rectangle and a triangle.

The area of the rectangle is 0.4 * 1.0 and the area of the triangle is 0.3 * 1.0 / 2. Add them together for a total of 0.55. Simple and straight forward.

MathWorld tells us that the formula for a right trapezoid is 1/2 * a * (h1 + h2), and 1/2 * 1.0 * (0.4 + 0.7) gives us the same result of 0.55.

With little effort, geometry offered us a couple of solutions to the problem.

The geometric solution.

Q: When should we use it?

A: IMHO, whenever we can.

Pros: Simple and straightforward.

Cons: None

Next, let's look to calculus for a solution.

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