Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped like a triangular prism, how much fabric will be left over?
height: 6 cm
width: 4 cm
length: 12 cm
Georgia Milestones Grade 7 Mathematics Formula Sheet
(1 point)
Responses
184 centimeters squared
184 centimeters squared
324 centimeters squared
324 centimeters squared
84 centimeters squared
84 centimeters squared
240 centimeters squared
240 centimeters squared
Skip to navigation
To calculate the total surface area of the triangular prism tent, we first need to find the surface area of each of the faces.
The triangle face has a base of 4 cm and a height (from the top point of the triangle to the base) of 6 cm. The formula for the area of a triangle is (1/2) x base x height.
Area of triangle face = (1/2) x 4 cm x 6 cm = 12 cm squared
Since there are two triangle faces, the total area for the triangle is 2 x 12 cm squared = 24 cm squared.
Next, we calculate the area of the rectangular faces. The front face is 4 cm x 6 cm = 24 cm squared, and the back face has the same dimensions, so the total area for the rectangular faces is 2 x 24 cm squared = 48 cm squared.
Lastly, we find the surface area of the 2 trapezoidal faces. Each face is a trapezoid with bases of 6 cm and 4 cm, and a height of 12 cm. The formula for the area of a trapezoid is (1/2) x (base1 + base2) x height.
Area of trapezoidal face = (1/2) x (6 cm + 4 cm) x 12 cm = (1/2) x 10 cm x 12 cm = 60 cm squared
Since there are two trapezoidal faces, the total area for the trapezoids is 2 x 60 cm squared = 120 cm squared.
Adding up all the areas: 24 cm squared (triangle) + 48 cm squared (rectangle) + 120 cm squared (trapezoid) = 192 cm squared
The total surface area of the tent is 192 cm squared. Since the initial piece of fabric Jordan purchased is 18 cm x 18 cm = 324 cm squared, the amount of fabric left over after making the tent is 324 cm squared - 192 cm squared = 132 cm squared.
Therefore, the correct response is: 132 centimeters squared
also, one side of the triangle (without doing anything to it) is: 7cm
If one side of the triangle is 7 cm, then to find the area of the triangle you will use the formula for the area of a triangle, which is (1/2) x base x height.
Given:
- One side of the triangle is 7 cm
- The height of the triangle is 6 cm
Area of triangle = (1/2) x 7 cm x 6 cm = 21 cm squared
Since there are two triangle faces, the total area for the triangle is 2 x 21 cm squared = 42 cm squared.
The rest of the calculations for the rectangular faces and trapezoidal faces remain the same.
Total surface area of the triangular prism tent is: 42 cm squared (triangle) + 48 cm squared (rectangle) + 120 cm squared (trapezoid) = 210 cm squared
The amount of fabric left over after making the tent is 324 cm squared (initial piece of fabric) - 210 cm squared = 114 cm squared.
Therefore, with one side of the triangle being 7 cm, the correct response for the amount of fabric left over is: 114 centimeters squared.
please round that to an answer
In that case, when rounded, the correct response is: 114 centimeters squared.
round it to one of these responses:
184 centimeters squared
184 centimeters squared
324 centimeters squared
324 centimeters squared
84 centimeters squared
84 centimeters squared
240 centimeters squared