Kym’s sawhorse is 39 inches tall, 27 inches long, and 19 inches wide. Its diagonal measurement, or the hypotenuse, is 40.14 inches. What is its total surface area? Round your answer to the nearest hundredth.
To find the surface area, we need to add up the area of each of the six faces.
The top and bottom faces are both 27 inches by 19 inches, so their combined area is:
2(27 in x 19 in) = 1026 square inches
The front and back faces are both 39 inches by 27 inches, so their combined area is:
2(39 in x 27 in) = 2106 square inches
The two side faces are both 39 inches by 19 inches, so their combined area is:
2(39 in x 19 in) = 1482 square inches
To find the total surface area, we add all of these areas together:
1026 + 2106 + 1482 = 4614 square inches
Therefore, the total surface area of the sawhorse is 4614 square inches (rounded to the nearest hundredth).
Use the image to answer the question.
A coordinate plane shows the x and y axes ranging from negative 6 to 6 in unit increments. Four points are plotted and labeled on the plane. The coordinates of the plotted points and the labels are as follows: left parenthesis 2 comma 1 right parenthesis is labeled as daisies, left parenthesis 5 comma 1 right parenthesis as roses, left parenthesis 5 comma 5 right parenthesis as lilies, and left parenthesis 2 comma 6 right parenthesis as sunflowers.
A map of a flower shop is shown. How far are the sunflowers located from the daisies? Each coordinate represents a foot.
(1 point)
Responses
5 feet
5 feet
3 feet
3 feet
4 feet
4 feet
7 feet
The distance between the daisies and sunflowers can be found by using the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) are the coordinates of the daisies and (x2, y2) are the coordinates of the sunflowers.
Plugging in the values, we get:
d = √((2 - 2)^2 + (6 - 1)^2)
d = √(0 + 25)
d = √25
d = 5
Therefore, the sunflowers are located 5 feet away from the daisies. Answer: \boxed{5\text{ feet}}.
Well, looks like Kym's sawhorse is trying to measure up! Let's calculate the total surface area using some mathematical comedy!
Now, to tackle the surface area, we need to consider all the sides of the sawhorse. It's like giving each side a ticket to the Surface Area Spectacular Show!
First, let's find the area of the rectangular tops. The length and width give us the area of one top, and we have two! So we get 27 x 19 x 2.
Next, let's calculate the area of the sides. We have four sides with dimensions of 27 x 39, but since two of them are the same, we'll add them just once and multiply by 2: 27 x 39 x 2.
Finally, we need to find the area of the ends, which are triangles. Since we have two of them, we'll calculate the area of one and multiply by 2. The base and height of each triangle are determined by the dimensions 19 and 39, so we have (1/2) x 19 x 39 x 2.
Now, it's showtime! Let's add all these areas together: (27 x 19 x 2) + (27 x 39 x 2) + ((1/2) x 19 x 39 x 2).
And after some calculations, the total surface area of Kym's sawhorse is approximately 4037.58 square inches. Ta-da!
Remember, though, that we rounded to the nearest hundredth, so don't forget to account for that. Enjoy your new knowledge and keep measuring with a smile!
To find the total surface area of Kym's sawhorse, we need to calculate the area of each face and then sum them up.
The sawhorse has six faces: top, bottom, front, back, left, and right.
To find the area of a rectangular face, we multiply its length by its width.
Area of top face = Length × Width
Area of top face = 27 inches × 19 inches = 513 square inches
Area of bottom face = Length × Width
Area of bottom face = 27 inches × 19 inches = 513 square inches
Area of front face = Length × Height
Area of front face = 27 inches × 39 inches = 1053 square inches
Area of back face = Length × Height
Area of back face = 27 inches × 39 inches = 1053 square inches
Area of left face = Width × Height
Area of left face = 19 inches × 39 inches = 741 square inches
Area of right face = Width × Height
Area of right face = 19 inches × 39 inches = 741 square inches
Now, let's calculate the diagonal measurement of each face using the Pythagorean theorem.
For the top face:
Diagonal of top face = √(Length^2 + Width^2)
Diagonal of top face = √(27 inches^2 + 19 inches^2) ≈ 33.61 inches
For the bottom face:
Diagonal of bottom face = √(Length^2 + Width^2)
Diagonal of bottom face = √(27 inches^2 + 19 inches^2) ≈ 33.61 inches
For the front face:
Diagonal of front face = √(Length^2 + Height^2)
Diagonal of front face = √(27 inches^2 + 39 inches^2) ≈ 47.43 inches
For the back face:
Diagonal of back face = √(Length^2 + Height^2)
Diagonal of back face = √(27 inches^2 + 39 inches^2) ≈ 47.43 inches
For the left face:
Diagonal of left face = √(Width^2 + Height^2)
Diagonal of left face = √(19 inches^2 + 39 inches^2) ≈ 43.13 inches
For the right face:
Diagonal of right face = √(Width^2 + Height^2)
Diagonal of right face = √(19 inches^2 + 39 inches^2) ≈ 43.13 inches
Now we have all the areas and diagonal measurements for each face. To find the total surface area, we sum up the areas of all the faces.
Total surface area = 2 × (Area of top face + Area of bottom face + Area of front face + Area of back face + Area of left face + Area of right face)
Total surface area = 2 × (513 square inches + 513 square inches + 1053 square inches + 1053 square inches + 741 square inches + 741 square inches)
Total surface area ≈ 6978 square inches
Therefore, the total surface area of Kym's sawhorse is approximately 6978 square inches.