# Composite Figures in Architecture

## Perimeter and Area of Composite Figures

Amber Stokes, Brittany VanCleave, Amber Stokes | Published: May 25th, 2022 by K20 Center

• Subject Mathematics
• Course Middle School Mathematics
• Time Frame 2-3 class period(s)
• Duration 120 minutes

### Summary

The lesson focuses on solving for perimeter and area of composite figures. Students will explore area and perimeter using pattern blocks to create unusual shapes, and then try to calculate the areas of these shapes. Next, students will learn about the real-life application of mathematics by watching a video about life as an architect. Students will then step into the role of an architect, creating the floor plans of their dream homes using basic shapes before calculating the area and perimeter of their peers' floor plans. This lesson includes optional modifications for distance learning. Resources for use in Google Classroom are included.

### Essential Question(s)

How can I use formulas to find the area and perimeter of an object with an unusual shape? How do the dimensions of a figure affect area and perimeter?

### Snapshot

Engage

Students complete the "What I Know" and "What I Want to Know" columns of an area and perimeter KWL chart.

Explore

Students use pattern blocks to find the area and perimeter of one of three unusual shapes.

Explain

Students explain how they arrived at the area and perimeter of each unusual shape. As a class, they learn and work through the formula for the area of a trapezoid.

Extend

Students create a house floor plan using rectangles, triangles, circles, and trapezoids. Students find the area and perimeter of their floor plans.

Evaluate

Students pass their floor plans to their group members, and then find the areas and perimeters of other students' floor plans.

### Materials

• Lesson Slides (attached)

• KWL Chart handouts (attached, one per student)

• Student Record Sheet handouts (attached, one per pair of students)

• Rulers

• Pattern blocks (optional)

• Design a House handouts (attached, one per student)

• Sticky notes

• Colored pencils or similar art supplies (optional)

### Engage

Use the attached Lesson Slides to guide the lesson. Begin with slide 2 and introduce the essential questions to students: How can you use formulas to find the perimeter and area of an object with an unusual shape? How do the dimensions of a figure affect the perimeter and area? Move to slide 3 to share the lesson objective: By the end of the lesson, students will be able to find the perimeter and area of composite figures using both pattern blocks and architecture designs.

Go to slide 4. Introduce students to the KWL Graphic Organizer strategy to activate prior knowledge about perimeter and area. Give each student a copy of the attached KWL Chart handout. Have students complete the K ("What I Know") and W ("What I Want to Know") columns. Ask volunteers to share a few things they wrote and facilitate a brief class discussion. Document what students share on a class chart.

### Explore

Move to slide 5. Sort students into pairs, and give each pair a set of pattern blocks, one copy (including all three unique shapes) of the attached Student Record Sheet handout, and a ruler. Invite students to create block figures based on the pictures. After they create their figures with the pattern blocks, have students use rulers to measure the figures. Students should record the perimeter and area of each figure on their handout. Formulas for calculating the perimeters and areas of various shapes are included on the slide as reminders.

### Explain

On slides 6-8, review the "butterfly," "lollipop," and "fish" pictures as a class and invite students to explain how they solved for each picture. Solicit a few answers from different members of the class to compare answers.

Move to slide 9. Using the diagram on the slide, show students how to solve for the area of a trapezoid with the provided formula. Select numbers to represent a, b, and h, and then work a sample problem with the students using those numbers. It is likely that students calculated the area of trapezoids in the Explore by splitting them into two triangles and a rectangle, but now they have a single calculation—as opposed to three—to arrive at the same answer.

Go to slide 10. Invite students to retrieve their KWL Charts and complete the L ("What I Learned") column. Allow enough time for students to do so, and then invite volunteers to share what they learned. As with the Engage part of the activity, document what students share on your class chart.

Ask students if they can think of a real-life scenario in which they could use what they learned about area and perimeter. Solicit a few answers from the class. Transition into the next activity by telling students that one real-life application for perimeter and area is in architecture and that they will be using area and perimeter to design their dream homes.

### Extend

Go to slide 11. Use the video link on the slide (or here), or the embedded version of the video below to show students the video "I Wanna Be an Architect: A Day In The Life Of An Architect."