The diagram shows a tent which has a rectangular base with vertical sides of height 2m, width 6m and length 8m, surmounted by a pyramid. The vertex,v, of the pyramid is 3m above the centre of the base of the tent
Calculate the area of the triangular face VEF
Calculate the area of the triangular face VFG.
The canvas on the sides and the roof is to be waterproofed at a cost of £1.25 per square metre.
Calculate the cost of waterproofing.
Thanks
I have no idea which vertices are VEF, but just draw a diagram and note that the distance from the center pole to the base of the triangle is 1/2 the side length adjacent to the base of the triangular face.
Then you can get the (slant) height of the triangle using the Pythagorean Theorem.
To calculate the area of triangular face VEF, we need to determine the height of the triangle.
First, let's find the length of EV, which is the distance from the vertex (V) to the center of the base. We're given that the vertex is 3m above the center of the base, and the height of the sides of the base is 2m. Therefore, EV would be (2m + 3m) = 5m.
Next, we find the base of the triangle, which is the width of the base of the tent. Given that the width is 6m, the base of the triangle would also be 6m.
To calculate the area of the triangle, we use the formula:
Area = (base × height) ÷ 2
Substituting the values, we get:
Area VEF = (6m × 5m) ÷ 2 = 30m²
So, the area of triangular face VEF is 30 square meters.
To calculate the area of triangular face VFG, we follow the same procedure.
First, let's find the length of EV, which we've already determined to be 5m.
Now, we find the base of the triangle, which is the length of the base of the tent. Given that the length is 8m, the base of the triangle would also be 8m.
Using the formula for the area of a triangle, we have:
Area VFG = (8m × 5m) ÷ 2 = 20m²
Therefore, the area of triangular face VFG is 20 square meters.
To calculate the cost of waterproofing, we need to find the total area of the canvas on the sides and the roof.
The area of the four sides can be calculated using the formula:
Area of a rectangle = length × width
Considering that the sides are rectangles, and the length and width are both given as 8m and 2m respectively, we find:
Area of sides = 2 × (8m × 2m) = 32m²
Next, we calculate the area of the roof, which is the rectangular base of the tent. Given that the width is 6m and the length is 8m, the area of the roof is:
Area of roof = 6m × 8m = 48m²
To find the total area of the canvas, we take the sum of the areas of the sides and the roof:
Total area of canvas = Area of sides + Area of roof = 32m² + 48m² = 80m²
Finally, we calculate the cost of waterproofing at £1.25 per square meter as follows:
Cost of waterproofing = Total area of canvas × Cost per square meter
= 80m² × £1.25/m² = £100
Therefore, the cost of waterproofing the tent's canvas on the sides and the roof is £100.