how do i solve?

Question

What is the best estimate for the area of the figure outlined in white if each light blue tile measures 3 units on each side? 

Answer 1

I would first start by counting the full boxes! We get a total of 8 boxes.

The two top left boxes account for 1 total box.

The two bottom right account for 1/2 a box. Add this half box to the top right Half box and you get yourself another 1 full box.

How many boxes total? 8+1+1= 10.

What is the total area of each box? Length * width we get 3*3 = 9

What is the total area of the region ? 10*9 = 90 square units is your answer!

Answer 2

For this problem, it would help to break the problem down into smaller pieces: squares, rectangles, and triangles. You should be able to solve this pretty quickly remembering that the area of rectangles is base * height and the area of triangles is 1/2 * base * height.

A more difficult question might be to measure the perimeter. For this case you should remember your Pythagorean triples of x, x, x√2 and x, 2x, x√3.

Good hunting!

Answer 3

There is one problematic area: the 2 blocks on the bottom right.

There are 8 whole blocks.

The upper left 2 blocks adds exactly one more block.

The block on the upper right adds 1/2 block.

If the lines in the lower right blocks intersect at the midpoint, they account for another 1/2 block.

That adds to 9 whole blocks, each of which contains 9 square units. Total 81 sq units.