WSP Isosceles Triangle Area

• ## Isosceles Triangle Area

Grade: 6th to 8th

Explore when an isosceles triangle obtains its maximum area.

This interactive is optimized for your desktop and tablet.

### Activity

 Web Sketchpad Copyright © 2015 KCP Technologies, a McGraw-Hill Education Company. All rights reserved. Release: 2015Q2, Semantic Version: 4.2.0, Build Number: 911.6-r, Build Stamp: dn.kcptech.com/20150706050244 Activity Contents Copyright © 2015 National Council of Teachers of Mathematics. All rights reserved.

### How to Use

• You can modify the length of the base by dragging Points A or C.
• You will not be able to modify the length of the congruent sides, which is fixed to 5 cm.
• As you modify the length of the base, observe the trace, which shows the relationship between the area of Triangle ABC, and the length of its base, Segment BC.

### Buttons

• Erase Traces will erase any traces that have been marked on the grid.

### Exploration

• When does Triangle ABC obtain its maximum area?
• What is the relationship between its sides?
• What is the relationship between the base and height?
• Construct a formal or informal proof as to when the maximum area of an isosceles triangle is obtained.
• Share a scenario where this would be applicable in real life.

### Objectives and Standards

NCTM Standards and Expectations
• Geometry / Measurement
• Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
• 6-8
• Geometry
• Measurement