Area of Triangles

To Find the Area of a Triangle by Discovery.

  • 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 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. 

To Investigate the different types of Triangles.

  • Moving any vertex of the triangle below to see different types triangles. ​
  • Observe the descriptions of the different triangles that pop up.

(A). 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.

(B). Find the areas of the triangles below. Show your reasoning.

(C). Find the area of the parallelogram below. Show your reasoning.

(D). 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.

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.