Given that there are 360 degrees in a quadrilateral, 

\(\displaystyle 50 + 110 +80 + 2w=360\)

\(\displaystyle 240+2w=360\)

\(\displaystyle 2w=120\)

\(\displaystyle w=60\)

The area of a rectangle is calculated by multiplying the length by the width. Here, the length is 7.5 and the width is 2, so the area will be 15. 

Given that the area is also equal to \(\displaystyle 5x\), the value of \(\displaystyle x\) will be 3, given that 3 times 5 is 15. 

The formula for the volume of a rectangular solid is \(\displaystyle Volume (V)=Length*Width*Height\).

Use the provided information from the question in the above formula and solve for the length.

• \(\displaystyle 40 in^3 = Length*2 in*5in\)
• \(\displaystyle 40in^{3}=Length*10in^{2}\)
• \(\displaystyle 4in=Length\)

Therefore, the length of the box is 4 inches. In answering this question, it is important to look at the units before selecting an answer. It is easy to be tricked into thinking that because the total answer is in cubic inches that it may be necessary to have square inches, but when multiplying three values, each with inches as their units, the units of the product will be cubic inches. 

The pool can be seen as a rectangular prism with dimensions \(\displaystyle 24\) meters by \(\displaystyle 14\) meters by \(\displaystyle 2.5\) meters; its volume in cubic meters is the product of these dimensions, which is 

\(\displaystyle 24 \times 15 \times 2.5 = 900\) cubic meter.

One cubic meter is equal to one thousand liters, so multiply:

\(\displaystyle 900 \times 1,000 = 900,000\) liters of water.

Multiply each dimension by \(\displaystyle 100\) to convert meters to centimeters:

\(\displaystyle 4.3 \times 100 = 430\)

\(\displaystyle 3.5 \times 100 = 350\)

Multiply these dimensions to get the area of the rectangle in square centimeters:

\(\displaystyle 430 \times 350 = 150,500\textrm{ cm}^{2}\)

The bottom of the swimming pool has area 

\(\displaystyle 50 \times 35 = 1,750\) square feet.

There are two sides whose area is 

\(\displaystyle 50 \times 5 = 250\) square feet,

and two sides whose area is 

\(\displaystyle 35 \times 5 = 175\) square feet.

Add the areas:

\(\displaystyle 1,750 + 250+ 250+ 175+175= 2,600\) square feet.

One one-gallon can of paint covers 350 square feet, so divide:

\(\displaystyle 2,600 \div 350 \approx 7.4\)

Seven full gallons and part of another are required, so eight is the correct answer.

To find the area of a rectangle, you must multiply the two different side lengths.  For this room the answer would be \(\displaystyle 192ft^{2}\) because \(\displaystyle 12*16=192\).

The area of the square, whose sides have length \(\displaystyle x\), is the square of this sidelength, which is \(\displaystyle x^{2}\). The area of the rectangle is the product of the lengths of its sides; this is \(\displaystyle 2x \cdot \frac{1}{2} x = 2 \cdot \frac{1}{2} \cdot x \cdot x = x^{2}\)

The square and the rectangle have the same area, so the correct response is 160.

Figure 1 is a rectangle divided into 24 squares of equal size; 3 of the squares are shaded, which means that \(\displaystyle \frac{3}{24} = \frac{3 \div 3}{24\div 3 } = \frac{1}{8}\) of Figure 1 is shaded.

Figure 2 is a circle  divided into 8 sectors of equal size; 1 is shaded, which means that \(\displaystyle \frac{1}{8}\) of Figure 2 is shaded.

Since the two figures are of the same area, the two shaded portions, each of which have an area that is the same fraction of this common area, must themselves have the same area. Since the shaded portion of Figure 1 has area 64, so does the shaded portion of Figure 2.

The area of a parallelogram is its base multiplied by its height - represented by \(\displaystyle b\) and \(\displaystyle h\) here:

\(\displaystyle A = bh = 16 \cdot 10 = 160\)

Note that the value of \(\displaystyle a\) is irrelevant.