4. Each small square in the graph paper represents 1 square unit. Find the area of each figure. Explain your reasoning.
A
B

A = 6.5

B = 10.

Step-by-step explanation:

First, remember that when we have a triangle of height H and base B, the area of the triangle is:

Area = B*H/2.

A:

First, count the complete squares:

We have 6 complete squares.

Now the diagonal part:

The diagonal connects a section of 1 by 3 squares, and the shaded area is a right triangle

Then the shaded area will be half of 1 by 3.

this is 1.5 squares.

The total area of A is:

6 + 1.5 = 7.5 squares.

B:

This is more complicated.

At the beginning, we have 4 completed squares in the top right.

At the left, we have a 2 by 4 = 8 square region, where the shaded part is only a triangle rectangle.

Then the area of this triangle is half of 8 squares:

8/2 = 4 squares.

Last, at the bottom, we have two times a 2 by 1 = 2 square region, where the shaded part is a triangle rectangle.

Then the area of each triangle is 2/2 = 1 square.

And we have two of them, so there are 2 squares here.

Then the total area is:

A = 4 + 4 + 1 + 1 = 10 squares.

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step-by-step explanation: