Question

1. What is the area of this polygon?

Answer 1

Answer:

1) 31.5

2) C) 37.5 units²

3) a) 14+16.25π units²

4) 25.5 square units

5) 40 units²

Step-by-step explanation:

1. The area of the polygon can be found by counting the number of unit squares inside the polygon.

We have 31.5 unit squares. Therefore the area is 31.5 square units.

2. We still count the square units. This time, we have 37.5 unit squares.

Therefore the area is 37.5 units²

The correct answer is C

3. The area of a semi-circle is given by

$\frac{\pi \: {r}^{2} }{2}$

From the diagram, the diameter of the semi- circle is

$d = \sqrt{ {4}^{2} + {7}^{2} }$

$d = 8.06$

This implies that:

$r = 4.03$

The area of the semi-circle is

$\frac{ {4 .03}^{2} \pi}{2} = 16.25\pi$

The area of the triangular part is ½*7*4=14 square units.

Therefore the area of the figure is:

14+16.25π square units

5. The area of the composite figure is the area of the triangular portion plus the area of the rectangular portion.

The area of the rectangular portion is 5*7=35 square units.

The area of the triangular portion is ½*2*5=5 square units.

The area of the composite figure is 5+35=40 square units.