A tent is a shape of a triangular prism resting on a rectangular base side pq congreubt to side pr pt is 1.5m
length of tent is 5m (tan 37* is o.75)
find area of canvas required for tent and volume of the tent
Answers
The required amount of canvas is approximately 14.115✓3 m².
The volume of the tent is approximately 2.812✓3 m³.
Given data :
Length of one side of the base triangle is 1.5 metres.
Length of the tent 5 metres.
• At first we have calculate the surface area of the tent.
(We will do the following calculations by assuming that the ground side of the tent is also covered by the canvas)
• Firstly,we have to calculate the area of the base triangle.
Now, it's obvious that the base triangles are equilateral triangles which have three equal sides of 1.5 metres.
• So,the area of the base triangle
= ✓3/4 × (side)²
= ✓3/4 × (1.5)²
= ✓3/4 × 2.25 m²
• Area of one rectangular side
= Base triangle length × Tent length
= 1.5 × 5
= 7.5 metres.
• The total surface area of the tent
= (2×Base area)+(3× Side area) [ A triangular prism has two base and three sides]
= (2×✓3/4×2.25)+(3×7.5)
= (✓3/2 × 2.25) + 22.5
= 1.125✓3+22.5
= 1.125 ✓3 + 12.990 ✓3
= 14.115 ✓3 m² (approx)
• The volume of the tent
= (Base area × height)
= (✓3/4 ×2.25×5)
= 2.812 ✓3 m³ (approx)