## Using Geometry in Design Problems

#### Aligned To Common Core Standard:

**Modeling Geometry** - HSG-MG.A.3

How is Geometry Used in the Design of Houses? Geometry is not just a branch of math. It is used for variety of other purposes. One such role is the designing of houses. If your question is how, let us tell you! Patterns and designs are found everywhere. Even in nature itself. Flowers, seashells, beehives, all are examples of natural patterns. Getting inspirations from these designs, humans created geometry, which has abundant techniques and methods to calculate various measurements that are necessary for constructing multiple buildings, big and small. Points, lines, angles, curves, two- and three-dimensional shapes, volumes, and proportions constitute the basics of home designs, and they are all calculated through geometry! For building our house walls, ceilings, length of our rooms, everything was calculated using geometry. Even the huge pyramids, cathedrals, and various other buildings have a wealth of geometry in them!

### Printable Worksheets And Lessons

- Candy Bar Step-by-step Lesson - Time to see how many candy bars you can shove in your closet.

- Guided Lesson - Shipping mobile phones, inheriting a water tower, and building tabletops. Geometry rocks!

- Guided Lesson Explanation - These problems each require you to think outside the box.

- Practice Worksheet - I do tend to gravitate towards three concepts.

- Matching Worksheet - The units make it simple, but they have to show their work.

#### Homework Sheets

There are 3 common themes that are in these types of problems.

- Homework 1 - You want to send some chocolates to your relatives. The chocolates are packed in boxes that are 3 feet long, 4 foot wide and 5 foot high. How many of these boxes can you pack into a carton which is 7 feet long, 7 feet wide, and 18 feet high?
- Homework 2 - Start by finding the total cubic footage of the carton.
- Homework 3 - See how many boxes you can fit into the area.

#### Practice Worksheets

I added images where I could fit them. I'd recommend that students always draw a picture when doing these problems.

- Practice 1 - Two carpenters decided to design dining table for a sale. The dimensions of the dining table are as shown.
- Practice 2 - A water company inherits a water tank; as seen below. The tank is 25 cm thick throughout the entire tank. One cubic foot of water equals 9 gallons.
- Practice 3 - Kelly is an exporter. She needs to send cakes to many different locations. Cakes are packed in boxes that are 8 inches long, 6 inches wide and 5 inches high. How many of these boxes can you pack into a big container that is 40 inches long, 25 inches wide and 30 inches high?

#### Math Skill Quizzes

Students should have some difficulty here. There is very normal and very Okay.

- Quiz 1 - How many of these cartons could you pack into a storage locker that is 80 inches long, 60 inches wide and 90 inches high?
- Quiz 2 - The tower is 15 feet thick throughout the entire tower. One cubic foot of water equals 9 gallons. How many gallons of water can be stored in the water tower?
- Quiz 3 - Two carpenters decided to design a door for a home.