A question like this can become a little bit simpler with a shift in perspective. If we draw a box around the figure (picture 1), we can look at its area as the area that's left when we chop off 4 triangular chunks. The length of the outer box is 8, and its width is 10, making its area 8 x 10 = 80 square units.
Next, we find the area of the 4 triangular chunks. From picture two, we have:
- A 2 x 2 triangle with an area of (1/2) x 2 x 2 = 2 square units
- A 6 x 6 triangle with an area of (1/2) x 6 x 6 = 18 square units
- Two 4 x 4 triangles with areas of (1/2) x 4 x 4 = 8 square units
Adding these together, we find the area of all of the triangular chunks to be 2 + 18 + 8 + 8 = 20 + 16 = 36 square units.
Now that we have the areas of the larger box and the triangular chunks, we can "cut off" those chunks by subtracting their area from the area of the boxes, leaving only the area of the original figure. Doing this, we find that area to be
80 - 36 = 44 square units.
