Given a rectangle, the general equation for the perimeter is \(\displaystyle P = 2l + 2w\) and area is \(\displaystyle A = lw\) where \(\displaystyle l\) is the length and \(\displaystyle w\) is the width.

Let \(\displaystyle x\) = width and \(\displaystyle x + 10\) = length

So the equation to solve becomes \(\displaystyle 40 = 2x + 2(x+10)\) so \(\displaystyle x = 5\) thus the width is \(\displaystyle 5\; m\) and the length is \(\displaystyle 15\; m\).

Thus the area is \(\displaystyle 5\cdot 15= 75 \; m^{2}\)

The area of a rectangle can be calculated by multiplying the lengths of two adjacent sides. All of the choices given lists sufficient information, with one exception. We examine each of the choices.

The lengths of one pair of adjacent sides: This choice is false, as is directly stated above.

The perimeter and the length of one side: Using the perimeter formula, you can find the length of an adjacent side, making this choice false.

The lengths of one side and a diagonal: using the Pythagorean Theorem, you can find the length of an adjacent side, making this choice false.

The lengths of one pair of opposite sides: this gives you no way of knowing the lengths of the adjacent sides. This is the correct choice.

Drawing a vertical line at the end of the side of length \(\displaystyle 20\) divides the shape into a rectangle and a right triangle.

The sum of the areas of the two shapes is the area of the polygon. Multiply the length of the rectangle by its width to find the area of the rectangle, and use the formula \(\displaystyle A = \frac{1}{2}bh\), where \(\displaystyle b\) is the base and \(\displaystyle h\) is the height of the triangle, to find the area of the triangle. Adding them together gives the answer.

\(\displaystyle A_{total}=A_{rec}+A_{tri}\)

\(\displaystyle A_{total}=(8*20)+\frac{1}{2}(5*8)\)

\(\displaystyle A = 180\)

To find the area of a rectangle, multiply its width by its height. If we know two sides of the rectangle that are different lengths, then we have both the height and the width.

\(\displaystyle 9\cdot 7=63\)

The area of a rectangle is found by multiplying the length by the width.

\(\displaystyle Area=l(w)\)

The length is 12 cm and the width is 7 cm.

\(\displaystyle 12\cdot 7=84\)

Therefore the area is 84 cm².

The area of any rectangle with length, \(\displaystyle l\) and width, \(\displaystyle w\) is:

\(\displaystyle A=l\times w\)

\(\displaystyle A=14\times 18\)

\(\displaystyle A=252\, in^2\)

Recall how to find the area of a rectangle:

\(\displaystyle \text{Area}=\text{length}\times\text{width}\)

Now, plug in the given length and width to find the area.

\(\displaystyle \text{Area}=2 \times 20=40\)

Recall how to find the area of a rectangle:

\(\displaystyle \text{Area}=\text{length}\times\text{width}\)

Now, plug in the given length and width to find the area.

\(\displaystyle \text{Area}=12 \times 10= 120\)

Recall how to find the area of a rectangle:

\(\displaystyle \text{Area}=\text{length}\times\text{width}\)

Now, plug in the given length and width to find the area.

\(\displaystyle \text{Area}=8 \times 30= 240\)

Recall how to find the area of a rectangle:

\(\displaystyle \text{Area}=\text{length}\times\text{width}\)

Now, plug in the given length and width to find the area.

\(\displaystyle \text{Area}=100 \times 4= 400\)