Area of parallelogram

Question

The area of a parallelogram is 123 cm^2 . Had the base been reduced by 4 cm, the area would have been less by 32 cm^2. Find the original base of the parallelogram.

Answer 1

Hi Sam,

 

This is basically an algebra problem that relies, a little, on some knowledge of geometry.  As with with all word problems, it's important to make sure you understand what the questions is asking.

 

First, the geometry part of the problem.  We know that parallelograms are four-sided polygons with area (A) = base (b) x height (h).  Rectangles, squares, and rhombuses are parallelograms, but it doesn't matter which type to calculate area:  it's always A =bh.

 

So for this parallelogram:

 

1) A = 123 cm^2

2)  123 cm^2 = bh

 

That's still two variables, though, so we can't solve it yet.  However:

 

3)  We also know that (b - 4)h = 123 cm^2 - 32 cm^2

4) Simplified, that's hb - 4h = 91 cm^2, and so hb = 91 cm^2 + 4h

 

We still have two variables, but since we now have two algebraic expressions for "bh," we can use substitution to solve for one of them:

 

5)  123 cm^2 = bh = 91 cm^2 + 4h

6)  123 cm^2 = 91cm^2 + 4h

7)  32 cm^2 = 4h

8)   8 cm^2 = h

 

Now that we have h = 4, solving for b is very easy:

 

9)  123 cm^2 = 4b

10) 15.375 = b

 

That's the answer.  To check it, though, we can use the other part of the problem, so:

 

15.375 - 4 cm^2 = 11.375

(11.375)8 = 91 cm^2

 

Got it!