Basic Math and Pre-Algebra For Dummies (86 page)

Divide 250 by 2.2 to get your answer:

Notice that I took the division out to one decimal place. Because the number after the decimal point is 6, I need to round up my answer to the next highest gram. (See Chapter
11
for more about rounding decimals.)

So to the nearest gram, Binky weighs 114 grams. As usual, the conversion chain doesn't change the value of the expression — just the unit of measurement.

Some geometry word problems present you with a picture. In other cases, you have to draw a picture yourself. Sketching figures is always a good idea because it can usually give you an idea of how to proceed. The following
sections present you with both types of problems. (To solve these word problems, you need some of the geometry formulas I discuss in Chapter
16
.)

Sometimes you have to interpret a picture to solve a word problem. Read the problem carefully, recognize shapes in the drawing, pay attention to labels, and use whatever formulas you have to help you answer the question. In this problem, you get to work with a picture.

Mr. Dennis is a farmer with two teenage sons. He gave them a rectangular piece of land with a creek running through it diagonally, as shown in Figure 
18-1
. The elder boy took the larger area, and the younger boy took the smaller. What is the area of each boy's land in square feet?

To find the area of the smaller triangular plot, use the formula for the area of a triangle, where
A
is the area,
b
is the base, and
h
is the height:

The whole piece of land is a rectangle, so you know that the corner the triangle shares with the rectangle is a right angle. Therefore, you know that the sides labeled 200 feet and 250 feet are the base and height. Find the area of this plot by plugging the base and height into the formula:

To make this calculation a little easier, notice that you can cancel a factor of 2 from the numerator and denominator:

The shape of the remaining area is a trapezoid. You can find its area by using the formula for a trapezoid, but there's an easier way. Because you know the area of the triangular plot, you can use this word equation to find the area of the trapezoid:

• area of trapezoid = area of whole plot – area of triangle
  

To find the area of the whole plot, remember the formula for the area of a rectangle. Plug its length and width into the formula:

Now just substitute the numbers that you know into the word equation you set up:

So the area of the elder boy's land is 62,500 square feet, and the area of the younger boy's land is 25,000 square feet.

Geometry word problems may not make much sense until you draw some pictures. Here's an example of a geometry problem without a picture provided:

In Elmwood Park, the flagpole is due south of the swing set and exactly 20 meters due west of the tree house. If the area of the triangle made by the flagpole, the swing set, and the tree house is 150 square meters, what is the distance from the swing set to the tree house?

This problem is bound to be confusing until you draw a picture of what it's telling you. Start with the first sentence, depicted in Figure 
18-2
. As you can see, I've drawn a right triangle whose corners are the swing set
(S),
the flagpole
(F),
and the tree house
(T)
. I've also labeled the distance from the flagpole to the tree house as 20 meters.

The next sentence tells you the area of this triangle:

Now you're out of information, so you need to remember anything you can from geometry. Because you know the area of the triangle, you may find the formula for the area of a triangle helpful: