# [SOLVED] Finding areas

• Feb 9th 2009, 08:11 PM
lucy2284
[SOLVED] Finding areas
Hi I need some more help with word problems. I don't know if I can get some help because there are drawings that go with it but I'll explain them as best as I can. Or maybe just some ideas on how to plug it into an equation.

1. Length and area. Find the length y in the figure. The area of the shaded region is given. both pictures are completely shaded. There is an attached picture.
• Feb 9th 2009, 08:45 PM
Soroban
Hello, Lucy!

Are you sure that you couldn't figure these out yourself?

Quote:

Find the length $\displaystyle y$ in the figure.
Code:

                  * - - - - - *                 * |          |               *  |          |             *    |          | y    Area: 120 in²           *      |          |         *        |          |       * - - - - - * - - - - - *             y          y

The triangle has area: .$\displaystyle \tfrac{1}{2}y^2$

The square has area: .$\displaystyle y^2$

The total area is 120 in²: .$\displaystyle \tfrac{1}{2}y^2 + y^2 \:=\:120 \quad\Rightarrow\quad\tfrac{3}{2}y^2 \:=\:120 \quad\Rightarrow\quad y^2 \:=\:80$

Therefore: .$\displaystyle y \:=\:\sqrt{80} \:=\:4\sqrt{5}\text{ in.}$

Quote:

Code:

                  * - - *                 * |    |               *  |    |             *    |    | y    Area: 1200 cm²           *      |    |         *        |    |       * - - - - - * - - *             y        1

The triangle has area: .$\displaystyle \tfrac{1}{2}y^2$

The rectangle has area: .$\displaystyle y\cdot1 \:=\:y$

The total area is 1200 cm²: .$\displaystyle \tfrac{1}{2}y^2 + y \:=\:1200 \quad\Rightarrow\quad y^2 + 2y - 2400 \:=\:0$

. . which factors: .$\displaystyle (y-48)(y+50) \:=\:0$

. . and has the positive root: .$\displaystyle y \:=\:48$

• Feb 10th 2009, 02:47 AM
lucy2284
questions and thanks yous for word problem help
Thank you so much for your help. I am extremely bad at word problems I have been working on these for the past three days and nothing came to me. I am also a little confused as to where the 2y and 2400 came from in B. Thank you again.