A new park is being built in the shape of a trapezoid, as show in the diagram below. The builders will cover the ground with a solid rubber surface to ensure the children playing have a safe and soft place to land when they jump or fall. How many square yards of rubber will be needed for this park?
The trapezoid has 10 yards on the top, 12.5 yards on the left, 6.4 yards on the right and 20 yards on the bottom
Please type only the number of square yards in the answer box.
Your answer may include a decimal. Do not round.
Formula: A= 12 (b1 +b2)(h)
My apologies for the error. Let's calculate the correct area of the trapezoid with the dimensions provided.
Using the formula for the area of a trapezoid:
A = 1/2 * (sum of the lengths of the bases) * (height)
Plugging in the values:
A = 1/2 * (10 + 20) * 12.5
A = 1/2 * 30 * 12.5
A = 15 * 12.5
A = 187.5 square yards
Therefore, 187.5 square yards of rubber surface will be needed for the park.
To find the area of a rhombus, you can use the formula:
Area = (diagonal1 * diagonal2) / 2
First, we need to calculate the diagonals of the rhombus. The diagonals of a rhombus bisect each other and are perpendicular. This creates right-angled triangles inside the rhombus.
Let's calculate the lengths of the diagonals first:
In a rhombus, the diagonals bisect each other and are perpendicular, creating 4 right-angled triangles.
The lengths of the sides of the rhombus are given as:
- Top side: 7 in
- Left side: 6 in (inside the shape)
- Bottom side: 12 in
Let's first find the height (one of the legs of the right-angled triangle) by using the left side (6 in) and top side (7 in) using the Pythagorean theorem:
height^2 = 7^2 - (6/2)^2
height^2 = 49 - 9
height^2 = 40
height ≈ √40
height ≈ 6.32 in
Now, we have one of the legs of the right-angled triangle as 6.32 in.
Next, we can find half of the bottom side (diagonal) which is a leg of the same right-angled triangle:
base = 12 in / 2
base = 6 in
Now, we can use these two legs to calculate the diagonal (hypotenuse) of this right-angled triangle using the Pythagorean theorem:
diagonal1^2 = height^2 + base^2
diagonal1^2 = 6.32^2 + 6^2
diagonal1^2 = 39.86 + 36
diagonal1^2 = 75.86
diagonal1 ≈ √75.86
diagonal1 ≈ 8.7 in
Now that we have diagonal1 (8.7 in), let's move on to find diagonal2.
Sometimes, the more convenient way to calculate the diagonals of a rhombus is to divide it into two congruent triangles by drawing a line from the vertex of the rhombus to the midpoint of the opposite side (like an altitude). The two right-angled triangles formed are exactly the same as the one we worked on.
The length of the diagonal2 = 2 * height (as it goes from top to bottom)
diagonal2 = 2 * 6.32
diagonal2 = 12.64 in
Now that we have both diagonals, we can calculate the area using the formula:
Area = (diagonal1 * diagonal2) / 2
Area = (8.7 * 12.64) / 2
Area = 110.088 / 2
Area ≈ 55.04 in^2
Therefore, the area of the rhombus is approximately 55.04 square inches.
Since the provided options are rounded, the closest option is 57 in^2 (option b).
thats not right
Find the area of the figure described.
an image of a rhombus is shown. with a 7 in. on the top, a 6 in. inside of the shape on the far left, and a 12 in. on the bottom
a. 114 in^2 a. 114 in^2 b. 57 in^2 b. 57 in^2 c. 25 in^2 c. 25 in^2 d. 12.5 in^2
The scale drawing of the rectangular classroom floor has dimensions of 8 inches by 5 inches. The actual length of the longer side of the floor is 32 feet.
What is the actual area of the floor in square feet? Responses
40 feet^2
240 feet^2
640 feet^2
92,160 feet^2
Question 2:
Show your work for this problem. Be sure to show each step and explain using math vocabulary.
max word limit is 10,000, but make it short
To find the actual area of the floor in square feet, we need to first determine the scale factor used in the drawing.
Given:
Scale drawing dimensions: 8 inches by 5 inches
Actual longer side length: 32 feet
To find the scale factor, we need to convert the inches in the scale drawing to feet to match the actual dimensions.
8 inches * (1 foot / 12 inches) = 2/3 feet
5 inches * (1 foot / 12 inches) = 5/12 feet
Now, we calculate the scale factor by dividing the actual length by the corresponding length in the scale drawing:
32 feet / (2/3 feet) = 32 * 3/2 = 48
32 feet / (5/12 feet) = 32 * 12/5 = 76.8
The scale factor is 48 for the longer side and 76.8 for the shorter side.
To find the actual area of the floor in square feet, we use the scale factor to convert from the scale drawing area to the actual area:
Actual Area = Scale Factor^2 * Scale Drawing Area
Actual Area = 48^2 * 5
Actual Area = 2304 * 5
Actual Area = 11520 square feet
Therefore, the actual area of the classroom floor is 11520 square feet. The closest response is 92,160 feet^2.
is the answer 640?
Apologies for the confusion in the previous response. Let's correct the calculation.
Given:
Scale drawing dimensions: 8 inches by 5 inches
Actual longer side length: 32 feet
First, we need to determine the scale factor for the dimensions.
The scale factor for the longer side:
32 feet / 8 inches = 4 feet per inch
The scale factor for the shorter side:
32 feet / 5 inches = 6.4 feet per inch
To find the actual area of the floor in square feet, we need to apply the scale factor to the scale drawing area:
Scale drawing area:
8 inches * 5 inches = 40 square inches
Convert the area of the scale drawing to square feet using the square inches to square feet conversion:
40 square inches * (1 square foot / 144 square inches) = 0.2777 square feet
Now, we use the area scale factor to find the actual area:
Actual area = (4 feet per inch * 6.4 feet per inch) * 0.2777 square feet
Actual area = 25.6 square feet * 0.2777 square feet
Actual area ≈ 7.11 square feet
Therefore, the actual area of the classroom floor is approximately 7.11 square feet which is not one of the given response options. The correct calculation indicates that the closest valid answer is 40 feet^2, so the correct answer is 40 feet^2.
show your work for the problem. Be sure to show each step and explain using math vocabulary
To find the actual area of the floor in square feet, we will follow these steps:
1. Determine the scale factor used in the scale drawing.
2. Calculate the actual area of the floor based on the scale factor.
Given:
- Scale drawing dimensions: 8 inches by 5 inches
- Actual longer side length: 32 feet
Step 1: Calculate the scale factor:
- Convert the inches in the scale drawing to feet to match the actual dimensions.
- For the longer side:
8 inches * (1 foot / 12 inches) = 8/12 feet = 2/3 feet
- For the shorter side:
5 inches * (1 foot / 12 inches) = 5/12 feet
- Calculate the scale factor by dividing the actual length by the corresponding length in the scale drawing:
Scale factor for the longer side = 32 feet / (2/3 feet) = 48
Scale factor for the shorter side = 32 feet / (5/12 feet) = 76.8
Step 2: Find the actual area of the floor:
- Calculate the area of the scale drawing:
Scale drawing area = 8 inches * 5 inches = 40 square inches
- Convert the scale drawing area to square feet:
Scale drawing area in square feet = 40 square inches * (1 square foot / 144 square inches) = 40 / 144 square feet ≈ 0.2777 square feet
- Find the actual area using the scale factor and the scale drawing area in square feet:
Actual area = 48 * 76.8 * 0.2777 square feet ≈ 822.14 square feet
Therefore, the correct actual area of the classroom floor in square feet is approximately 822.14 square feet, which is not one of the provided response options.