Question

I got homework and I need help with it and starr testing is soon so I need big help

Answer 1

Hello there. To solve this question, we'll have to remember some properties about finding the area of a plane figure.

Given the following figure made by two congruent squares and a parallelogram:

We have to find the total area of the figure in square meters.

First, remember the formula for the area of a square with side length L:

Thinking of the square as full of strips with length L, in the direction pointed by the blue line, we run all the square (you can also think of it as filling the square with strips), hence the total area will be given by:

`Area_(\square)=L\cdot L=L^2`

Now, for the parallelogram:

Think of the right triangle in red as a piece of the parallelogram, that we can move in the following way:

Hence it turns to be the same as a rectangle and its area can be found in the same manner as the square, therefore we have

`Area_(rectangle)=L\cdot h=A_(parallelogram)`

In this case, the side length of the squares is equal to 3 m, the side length of the parallelogram is 6 m and its height is 2.8 m.

The total area will be given by the expression:

`A_(parallelogram)+2\cdot A_(\square)`

Using the formulas and plugging the values mentioned above, we'll get

`6\cdot2.8+2\cdot3^2`

Square the number, multiply the terms and add the values

`\begin{gathered} 6\cdot2.8+2\cdot9 \\ 16.8+18 \\ 34.8\text{ m\textasciicircum2} \end{gathered}`

This is the total area of the figure and it is the answer contained in the c) option.