The Math Helper Book

Area Word Problems

Let's face it, we're not always going to be given super simple math problems where we only have to worry about numbers. A lot of the time you will be faced with more real-life application problems, especially if you're using math outside of a classroom setting. These problems are called word problems, and they're a bit more difficult to understand for most people.

What makes them harder? I've found that the main challenges are:
1. Figuring out what the problem is asking.
And
2. Knowing how to find what it's asking.

Here's an example of a word problem:

Example #1
Becky has a triangular lawn with these dimensions:

If one bag of grass seed can cover 20 square meters, how many bags does she need to buy to fill her whole lawn with grass?

What do you do first? You pick apart the problem, finding all the useful information. If we want to know how much grass seed is needed, we must know two things:
1. How much area one bag covers.
2. How much area needs to be covered in total.

We are already given the answer for #1. One bag covers 20 square meters. We are not directly given #2, but we can find it by calculating the area using the measurements and the area formula.

Now we know #2. The total area we need to cover is 200 square meters. One bag covers only 20, so we multiply it by something to equal two hundred.

There you have the answer! You need 10 bags to cover the lawn.

*Note*: Always keep in mind what the problem asks for. If you only solve for the area of the lawn and put that as your answer, you will not be responding to the question correctly. If it asks for bags of seed, answer in bags of seed!

Example #2
Becky wants to replace the grass in her 200 square meter lawn with gravel. Each gravel bag covers 10 square meters. This time she wants to add a shed with the dimensions below. No gravel will be placed where the shed stands. Each bag of gravel costs $15. How many bags are needed to cover the lawn?

I threw a few curves at you in this problem, so don't be fooled! First, remember when I said you need to pick apart a problem for all the important information? Well, sometimes you'll encounter a problem that gives you more information than you need. The problem above is an example of this. Can you find the unnecessary information? Try to guess before I tell you.

The useless information is the cost of each bag. If you got it, good for you! Nowhere in the problem does it ask for something involving cost, so you can disregard it.

Now that we've found the good information, we can do the problem. It's very similar to example number one. You're still finding the same things:
1. How much area one bag covers.
2. How much area needs to be covered in total.

You are given #1 again: one bag covers 10 square meters. You are only given part of #2. The lawn is 200 square meters, but that is not the area you need to cover. There is a shed under which you will not put anything. So in order to find the area you really must cover, find the area of the shed using the measurements and the rectangular area formula, then subtract it from the area of the lawn.

Now that you have area needed to be covered as 160 square meters, you can divide this by the amount one bag of gravel covers (10 square meters) and get your answer.

Becky needs 16 bags of gravel.

That's all I have for now! If you'd like any more examples in this subject, let me know. As of now, remember that the single greatest step in solving any word problem is picking the question apart to find out just what it's asking.

Have a good day, and remember to smile!

:) Your Kiwi Tutor