Each of the figures of which the area has to be determined can be divided into rectangles and triangles. The area of a rectangle with sides of length a and b is A = a*b. And the area of a triangle with base b and height h is `A = (1/2)*b*h` .

To determine the area of figure a, consider a rectangle from which two triangles have been cut out. The length of the sides of the rectangle are 5 units and 5 units. From this, two triangles have been cut. The base and height of these is 5 units and 1 unit respectively. As each unit is equal to 0.5 cm, the area of figure a is `0.5^2*(5*5 - 2*((1/2)*1*5))` = 0.25*(25 - 5) = 0.25*20 = 5 cm^2.

Similarly, figure b is a rectangle with sides 3 and 4 from which a triangle with base 4 and height 1 has been cut. The area of the figure is `0.25*(3*4 - (1/2)*1*4)` = 0.25*(12 - 2) = 2.5 cm^2

The area of figure c is `0.25*(3*2 + 1*1 + (1/2)*3*2)` = 0.25*(6 +1+3) = 2.5 cm^2

The area of figure d is `0.25*(2*13 - (1/2)*1*2 - (1/2)*1*3)` = 0.25*(26 - 1 - 1.5) = 5.875 cm^2

The area of figure e is `0.25*(2*6+(1/2)*2*2 + (1/2)*2*2 + 1*2 + (1/2)*1*2) ` = 0.25*(12 + 2 + 2 + 2 + 1) = 0.25*19 = 4.75 cm^2

The area of figure f is `0.25*(3*4 + (1/2)*1*4 + 1*3 + (1/2)*1*1 + (1/2)*1*3)` = 0.25*(12+2+3+.5+1.5) = 0.25*19 = 4.75 cm^2

The area of figure g is `0.25*(2*9 + (1/2)*1*2 + (1/2)*2*2 + (1/2)*3*2)` = 0.25*(18 + 1+ 2+ 3) = 6 cm^2

Hey

The method that the home work instructs you to use is counting squares. It's pretty simple to do.

Let's look at (a) first.

- First count all of the full squares enclosed in the shaped. That gives you 15 square units.

- Now let's count the squares that are not completely enclosed in the shape and sort of merge them with other not fully enclosed squares to give us a full square.

for example, starting from the top left, the first and third squares would make one full square. Similarly, squares four and five in this row would also make one full square.

If you're following what I'm saying and you continue for the rest of incomplete squares, you should get 5 full squares from the incomplete squares.

Great!

Now the area of figure (a) would be 15 square units + 5 square units = 20 square units.

You will have to apply the same method for the other figures.