Three feet make a yard, so the length and width of the pool are  yards and  yards, respectively. Since the dimensions of the tarp must exceed those of the pool by at least one yard, the tarp must be at least  yards by  yards; but since both dimensions must be multiples of three yards, we take the next multiple of three for each.

The tarp must be 18 yards by 15 yards, so the area of the tarp is the product of these dimensions, or

 square yards.

The shaded portion of the entire triangle is similar to the entire large triangle by the Angle-Angle postulate, so sides are in proportion. The short leg of the blue triangle has length 20; that of the large triangle, 30. Therefore, the similarity ratio is . The ratio of the areas is the square of this, or , or . 

The blue triangle is therefore  of the entire triangle, or  of it.

If we see hypotenuse  as the base of the large triangle, then we can look at the segment perpendicular to it, , as its altitude. Therefore, the area of  is

.

, as the length of the altitude corresponding to the hypotenuse, is the geometric mean of the lengths of the parts of the hypotenuse it forms; that is, the square root of the product of the two:

The area of  is therefore

Three feet make a yard, so the length and width of the pool are  yards and  yards; the area of the pool, and that of the tarp needed to cover it, must be the product of these dimensions, or

 square yards. 

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of ten, which is 200 square yards.

The area of , being right, is half the products of its legs, which is:

The area of  is one half the product of its base and height; we can use its hypotenuse  as the base and  as the height, so this area is

Therefore, in terms of area,  is  of .

, as the length of the altitude corresponding to the hypotenuse, is the geometric mean of the lengths of the parts of the hypotenuse it forms; that is, it is the square root of the product of the two:

.

The areas of  and , each being right, are half the products of their legs, so:

The area of  is 

The area of  is 

The ratio of the areas is  - that is, 4 to 1.

Polygon  is a composite of  and Square ; its area is the sum of the areas of the two figures.

 is a right triangle; its area is half the product of its legs, which is 

 is both one side of Square  and the hypotenuse of ;  its hypotenuse can be calculated from the lengths of the legs using the Pythagorean Theorem:

.

Square  has area the square of this, which is 89.

Polygon  has as its area the sum of these two areas:

.

Write the formula for the area of a circle.

Substitute the diameter and solve.

Because we know the perimeter is 36 inches, we can determine the length of side w based on the equation of the perimeter of a rectangle:

Side w is 6 in long.

Now that we know that side w is 6 inches long, we have everythinng we need to calculate the area of the rectangle. 

The area of the rectangle is 72 in²

A kite is a four-sided shape with straight sides that has two pairs of sides. Each pair of adjacent sides are equal in length. A square is also considered a kite.