Cardboard costs $0.002 per square centimeter. How much will Alan spend to build the following figure out of cardboard? Round your answer to the nearest cent.
The figure appears to be composed of a square and four triangles. The side of the square is 6 decimal point 8 centimeters and a triangle is placed above it such that the base of the triangle and the side of the square coincide. Three triangles are placed to the right of this triangle adjacent to each other such that their sides coincide. The height of each triangle is labeled as 7 decimal point 5 centimeters.
I got 0.13
Well, let's break it down! The area of the square is simply the side length squared. So, the area of the square is (6.8 cm)^2. As for the triangles, each triangle has a base equal to the side length of the square, which is 6.8 cm, and a height of 7.5 cm.
The area of each triangle is (1/2) * base * height. Thus, the area of each triangle is (1/2) * 6.8 cm * 7.5 cm. Since there are four triangles, the total area of the triangles is 4 * (1/2) * 6.8 cm * 7.5 cm.
Now, we can calculate the total area of both the square and the triangles by adding the areas together. After that, we multiply the total area by the cost per square centimeter to find how much Alan will spend.
So, the total cost will be (total area) * ($0.002/cm^2). Rounded to the nearest cent, Alan will spend approximately (total cost in cents).
But, before I do that calculation, let me just say... this figure seems pretty "triangular." I bet it's a great pick for anyone who wants to feel "shapely" and "squarely" in style. Alright, here we go!
Area of square = (6.8 cm)^2 = 46.24 cm^2
Area of each triangle = (1/2) * 6.8 cm * 7.5 cm = 25.5 cm^2
Total area of triangles = 4 * (1/2) * 6.8 cm * 7.5 cm = 102 cm^2
Total area = Area of square + Total area of triangles = 46.24 cm^2 + 102 cm^2 = 148.24 cm^2
Total cost = (Total area) * ($0.002/cm^2) = 148.24 cm^2 * $0.002/cm^2 = $0.29648
Rounded to the nearest cent, Alan will spend approximately $0.30. So, my friend Alan will need to whip out only 30 cents (or maybe even try to find some in his couch cushions!) to build this masterpiece.
To find out how much Alan will spend to build the figure, we need to calculate the total area of the square and the four triangles, and then multiply that by the cost of cardboard per square centimeter.
Let's calculate the areas step by step:
1. Calculate the area of the square:
The side of the square is given as 6.8 centimeters. To find the area of a square, we square the length of one of its sides. So, the area of the square is 6.8 cm * 6.8 cm = 46.24 square centimeters.
2. Calculate the area of one triangle:
The base of the triangle is the same as the side of the square, which is 6.8 centimeters. The height of each triangle is given as 7.5 centimeters. To find the area of a triangle, we multiply the base by the height and divide by 2. So, the area of one triangle is (6.8 cm * 7.5 cm) / 2 = 25.5 square centimeters.
3. Calculate the total area of the four triangles:
Since there are four triangles in total, we need to multiply the area of one triangle by 4. So, the total area of the four triangles is 25.5 square centimeters * 4 = 102 square centimeters.
4. Calculate the total area of the figure:
To find the total area of the figure, we need to add the area of the square to the total area of the four triangles. So, the total area of the figure is 46.24 square centimeters + 102 square centimeters = 148.24 square centimeters.
5. Calculate the cost:
The cost of cardboard per square centimeter is given as $0.002. To calculate the total cost, we multiply the total area of the figure by the cost per square centimeter. So, the total cost is 148.24 square centimeters * $0.002 = $0.29648.
Rounding to the nearest cent, Alan will spend approximately $0.30 to build the figure out of cardboard.
Question 4 of 16
Construction paper costs $0.006 per square centimeter. How much will Susanna spend to build the figure out of construction paper? Round your answer to the nearest cent.
The figure shows a right pentagonal pyramid composed of a pentagon and triangles. The base of the triangle is 8 centimeters and height are 17 decimal point 2 centimeters. The perpendicular distance from the center of the pyramid to any of its sides is labeled as 8 centimeters.
A.
$1.06
B.
$2.71
C.
$4.46
D.
$5.42
you seem to have the base and height for each triangle.
So, add up all the areas, and add the area of the square.
Then just multiply the area by 0.002
What do you get?