A triangular shelter has a base width of 2 m, a height of 2 m, a length of 3 m and hypotenuse 2.8 m.
a) Every edge of shelter is to be sealed with tape.What length of tape is required.
b) The shelter tag says that is occupied 10,000L of space. Show showing working steps.
(a) draw a picture. You need tape along all the edges. That is,
2 triangles with sides 2, 2.8, 2.8
3 edges of length 3
So, add 'em up
(b) what is the question?
a) To find the length of tape required to seal every edge of the shelter, we need to calculate the perimeter of the triangular shelter.
The perimeter of a triangle is found by adding the lengths of all its sides. In this case, we need to determine the lengths of the three sides of the triangular shelter.
Given:
Base width = 2 m
Height = 2 m
Length = 3 m
From the given dimensions, we can determine that the triangular shelter is a right-angled triangle (since the base and height are at right angles). Using the Pythagorean theorem, we can find the length of the hypotenuse.
Using the formula:
Hypotenuse^2 = Base^2 + Height^2
Plugging in the values:
2.8^2 = 2^2 + 2^2
7.84 = 4 + 4
7.84 = 8
Since the equation is not balanced, there seems to be an error in the given dimensions. Please reconfirm the dimensions so that the Pythagorean theorem can be applied correctly.
b) To calculate the occupied space of the shelter, we need to find the volume. The volume of a triangular shelter can be determined by multiplying the area of the base (which is a triangle) with the length.
Given:
Base width = 2 m
Height = 2 m
Length = 3 m
Since the base of the shelter is a triangle, we can find its area using the formula:
Area = (base width * height) / 2
Plugging in the values:
Area = (2 * 2) / 2
Area = 4 / 2
Area = 2 m^2
Now, we can find the volume by multiplying the base area with the length:
Volume = Area * length
Volume = 2 * 3
Volume = 6 m^3
Therefore, the shelter is occupied by 6 cubic meters (6,000 liters) of space.