Today's Triangle Investigation

Yesterday we worked with finding the are of right triangles.  Students noticed that two right triangles made a rectangle, so they came to the conclusion you could multiply the base times the height of the right triangle and then divide by two (since the base times the height gives you the area of the quadrilateral...but each triangle only takes up half of the quadrilateral).  Our formula for finding the area of a right triangle looked something like (b x h)/ 2 or 
1/2 x b x h


Today students looked into acute triangles.  We found two different ways to find the area of acute triangles.  Take a look at the example below.

One way would be to look at it as two right triangles (since we already know how to find the area of those!).  You could find the area of the triangle with the base of 34m and height of 32m...take 32 x 34 / 2 or 1/2 x 32 x 34.  The area of that right triangle is 544m2 (the last 2 should be an exponent!).  Then the area of the other right triangle is 736m2.  So, add that together to get 464 square meters for the area of the whole triangle.

Another way to look at it is that we discovered that two acute triangles make a parallelogram.  So, we can take the height ( not a side measurement!) and multiply it by the whole base, and then divide by two.  So, we could do 32 x (34 + 12) /2 or 1/2 x 46 x 32..so 736 square meters.