# Area of Triangles

Warmup

Activity #1

`Find the Area of a Triangle (Discovery).`

A triangle is a basic shape in geometry with three edges and three vertices. Calculating the area is an elementary problem encountered often in many different situations. The base and the height are used to find the area. In this activity, you are going to discover how to find the area of a triangle in another way. See below. • Interact with the applet below for a few minutes.  Be sure to move the VERTICES of the triangle around each time before you move the black slider.
• Answer the questions that appear below the applet.
1. What LARGER FIGURE was formed when the slider reached its end? How do we know this to be true?​
2. How does the area of the original triangle compare with the area of this LARGER FIGURE?​
3. How do we find the area of this LARGER FIGURE? What is the formula we use to find it? ​
4. Given your responses to (2) & (3), write a formula that gives the area of JUST ONE of these congruent triangles.

Activity #2

` Investigate the Different Types of Triangles.`

Triangles are classified as follows:

Based on their sides, we have; Equilateral triangle, Isosceles triangle, Scalene triangle. Based on their angles, we have; Acute-angled triangle also called Acute triangles, Obtuse-angled triangle also called Obtuse triangle, and Right-angled triangle also called Right triangle. Check that out on the applet below. • Move any vertex of the triangle below to see different types triangles. ​
• Observe the descriptions of the different triangles that pop up.

There are 10 slides on the question set below. Use the forward arrow at the bottom to navigate the slides.

Activity #3

`Relate the Area of a Triangle to that of a Parallelogram.`

Since a parallelogram is made of two congruent triangles, the area of the triangle can be found in relation to the area of the parallelogram. In this activity, you are going to find the area of a parallelogram using a triangle. Han made a copy of Triangle M and composed three different parallelograms using the original M and the copy.

(1). For each parallelogram Han composed, identify a base and a corresponding height, and write the measurements on the drawing.

(2). Find the area of each parallelogram Han composed. Show your reasoning.

Find the areas of the triangles below. Show your reasoning.

Find the area of the parallelogram below. Show your reasoning.

Take the small triangle and the trapezoid, and rearrange these two pieces into a different parallelogram. Find the area of the new parallelogram you composed. Show your reasoning.

(1). How do you think the area of the large triangle compares to that of the new parallelogram: Is it larger, the same, or smaller? Why is that?

(2). Find the area of the large triangle. Show your reasoning.

Challenge #1

Challenge #2

Challenge #3

Find the estimated area of the triangle below by counting the enclosed squares. Hint: Count only squares that have most part enclosed within the figure.