How to find the area of a figure - HSPT Math

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 50 inches for our problem. Its total area would be 50 * 50 or 2500 in2.

Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr2 or π * 252 = 625π in2. Therefore, the area remaining would be 2500 - 625π. The cost of the waste would be 0.2 * (2500 – 625π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 5 from our subtraction. This would give us: 0.2 * 5 * (500 – 125π). Since 0.2 is equal to 1/5, 0.2 * 625 = 125. Therefore, our final answer is: 500 – 125π dollars.

Using the Pythagorean Theorem, the diameter of the circle (also the diagonal of the square) can be found to be 4√2. Thus, the radius of the circle is half of the diameter, or 2√2. The area of the circle is then π(2√2)2, which equals 8π. Next, the area of the square must be subtracted from the entire circle, yielding an area of 8π-16 square inches.

If you answered that the whirlpool’s area is 18.84 feet and therefore fits, you are incorrect because 18.84 is the circumference of the whirlpool, not the area.

If you answered that the area of the whirlpool is 56.52 feet, you multiplied the area of the whirlpool by 1.5 and assumed that that was the correct area, not the legal limit.

If you answered that the area of the backyard was smaller than the area of the whirlpool, you did not calculate area correctly.

And if you thought the area of the backyard was 30 feet, you found the perimeter of the backyard, not the area.

The correct answer is that the area of the whirlpool is 28.26 feet and, when multiplied by 1.5 = 42.39, which is smaller than the area of the backyard, which is 56 square feet.

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 88 inches for our problem. Its total area would be 88 * 88 or 7744 in2.

Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr2 or π * 442 = 1936π in2. Therefore, the area remaining would be 7744 – 1936π. The cost of the waste would be 0.25 * (7744 – 1936π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 4 from our subtraction. This would give us: 0.25 * 4 * (1936 – 484π). Since 0.25 is equal to 1/4, 0.25 * 4 = 1. Therefore, our final answer is: 1936 – 484π dollars.

First we will calculate the total area of the placemat:

Next we will calculate the area of the circular place

And

So

We will subtract the area of the plate from the total area

The formula for the area of a circle is

Allen has been running for 10 minutes since he lost his keys at 3m/s. This gives us a maximum distance of from his current location. If we move 1800m in all directions, this gives us a circle with radius of 1800m. The area of this circle is

Our answer, however, is asked for in kilometers. 1800m=1.8km, so our actual area will be square kilometers. Since he can search 1 per hour, it will take him at most 10.2 hours to find his keys.

To find the area of a circle you must plug the radius into in the following equation

In this case the radius is 7 so we plug it into to get

We then multiply it by pi to get our answer

To solve this question you must know the formula for the area of a rectangle.

The formula is

In this case the rectangle is a square so we can plug in the side length for both base and height to yield

Perform the multiplication to arrive at the answer of

Let be the radius of the circle. The area of the circle is

is also the sidelength of the equilateral triangle. The area of the triangle is

The percent of the circle covered by the triangle is:

The area of Julie's lawn is square feet. The amount of grass seed she needs is pounds. This requires three fifty-pound bags, the most economical option since it is cheaper to buy a fifty-pound bag for $66 than five ten-pound bags for $100.00. Julie will spend

Each side can be divided into three 3-foot sections. This gives a total of squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is

,

and the area of the square is

The square, therefore, takes up

of the entire figure.

The large rectangle has length 80 and width 40, and, consequently, area

.

The white region is a rectangle with length 30 and width 20, and, consequently, area

.

The white region is

of the large rectangle.

The area of a square is:

Substitute the length and simplify.

The area of a rectangle is

.

So for this you just multiple those two values together to get,

.

Remeber that the units of area are squared.

The area of a triangle is

.

is equal to the base multiplied by the height.

So you still need to multiple by or divide by .

This gives you an actual area of .

Therefore the statement is false.

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together.

A square with area 64 has as the length of one of its sides the square root of this area, which is . The length of a diagonal of a square is times this sidelength, so the square has diagonals of length .

25% of this is

.