# Formula for the Area of a Triangle

Warmup

Activity #1

 Identify a Base and a Corresponding Height of a Triangle.

Unless you are counting the squares that are enclosed within a triangle, the length of the base and the height of the triangle are needed if you have to find the area by calculation. In the applet below, you are going to locate the corresponding height of a triangle for a given base. • For each triangle below, identify a base and a corresponding height.
• Record the lengths and the areas of the triangles in the table below.
• In the last row, write an expression for the area of any triangle, using b and h.
• For each triangle below, circle a base measurement that you can use to find the area of the triangle. Note: You can access tools by a a click on Now, find the area of any three triangles. Show your reasoning.

Activity #2

 Investigate Why the Area of a Triangle is ( base x height.)

We already know that a parallelogram is composed of two congruent triangles. So its area is found in relation to the area of a parallelogram. In this activity, you are going to investigate how this comes about. • The parallelogram is decomposed into two triangles. Move the slider from the right position to the left.​
• Compare the area of the original figure to that of the final figure.

Make sure to navigate to all the slides below.

Activity #3

Explore the Area of Triangles.

Follow the instructions below and interact with the applet to explore the area of a triangle. • Move points A, B, and C. ​
• Observe the length of the base and height. ​
• Observe the area of the triangle.
1. What do you observe when you keep the base horizontal and slide point A left or right? ​
2. Does the area agree with your visual count of the squares inside the triangle?

Challenge #1

Tiana is making a shelf in the shape of a triangle to fit in the corner of her reading room. The triangle’s base is 16 inches long, and its area is 96 square inches.

Challenge #2

Andre drew a line connecting two opposite corners of a parallelogram. Select all true statements about the triangles created by the line Andre drew.

Challenge #3

The triangle on all the slides below is a right triangle.

Make sure to navigate through all the slides.