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Word Problems
Geometry Problems: At a Glance

Introduction to Geometry Problems:

Geometry problems are great, because they often come with pictures. Who doesn't like pictures? We especially like the ones by the late, great Maurice Sendak, but you won't see any of them in this section. Sorry.

Sample Problem

Find the area of the shape shown below, which consists of a triangle and a semicircle:

(Area of shape) = (Area of triangle) + (Area of semicircle).

We know how to find the area of a triangle:


The height of the triangle is 5, and the base is 10 (the diameter of the circle). Therefore, the area of the triangle is


We also know how to find the area of a semicircle. We know how to find the area of a circle, and the area of a semicircle is half that, right? Like a semi is half a truck? Wait a second...


Since the radius of this semicircle is 5, the area is


That makes the area of the entire shape:

(Area of shape) = (Area of triangle) + (Area of semicircle).

or, plugging in what we know,


That's as nice as this answer will ever be if we don't want to round things. As it happens, we're not in much of a rounding "mood" at the moment, so yeah, we're done.

When geometry problems don't come with pictures, we can often draw our own pictures anyway. Our lines may not be as perfectly straight as those generated by a computer, but at least they will have that personal touch that may be otherwise lacking. In fact, you may want to sign and date it in case your mom wants to post it on the fridge for a few months.

Geometry Problems Practice:

Example 1

A rectangular box has height 14 and a base with dimensions 8 by 12. What is the volume of the box?