Question

Can you please help me

Answer 1

EXPLANATION

The area of the figure can be obtained by applying the following relationship:

`Area_(paralle\log ram)=base\cdot height`

Where b=base and height=h

In order to find the height, we need to apply the trigonometric relationship:

`\sin 45=\frac{opposite}{\text{hypotenuse}}=\frac{height}{\text{diagonal}}=(h)/(6.4)`

Multiplying both sides by 6.4:

`6.4\cdot\sin 45=h`

Solving the argument:

`6.4\cdot0.65=h`

Switching sides:

`h=4.16\text{ inches}`

Now that we have the height, we can compute the area as follows:

`\text{Area}_{\text{parallelogram}}=12.8in\cdot4.16in=53.24in^2`

The answer is 53.24 squared inches.