 IGD Area of a Triangle

• ## IGD: Area of a Triangle

Grade: 3rd to 5th, 6th to 8th

How Do You Find the Area of a Triangle?

To find the area of a triangle, find a way to make it look like a shape for which you already know how to find the area. Try to make a parallelogram using a copy of the triangle.

### Instructions

The goal is to create a parallelogram by using a copy of any triangle.

• Change the size and shape of triangle ABC by dragging points A, B, and C.
• Click the Make Copy button to make a copy of the blue triangle. Translate the green copy using point D, and rotate it using point E.
• The Show Dimensions button will complete the problem for you.
• The Show Dimensions button indicates the dimensions needed to find the area, and the Start Over button resets the drawing.

### Exploration

Use the Make Copy button to create a green copy of the blue triangle. Try to arrange the two triangles to form a parallelogram. Translate the green copy using point D, and rotate it using point E. If you need help, use the First Move and Second Move buttons to show one way of making a parallelogram. There are also two other ways—can you find them?

• What measurements on the triangle do you need to make in order to find the Area of a Parallelogram?
• What is the area of the triangle?

### 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.
• 3-5
• 6-8
• Geometry