Scenario: Architectural Design - Design triangular structures using area and perimeter calculations!
You're designing a triangular roof for a small building. The roof has a base of 12 meters and a height of 8 meters. You need to calculate the area for roofing materials and the perimeter for the trim.
Questions:
1. How much roofing material do you need? (Area)
2. How much trim do you need for the edges? (Perimeter)
Visual representation of the triangular roof
Step 1: Calculate the area (roofing material needed)
Area = ½ × base × height
Area = ½ × 12 m × 8 m
Area = ½ × 96 m² = 48 m²
Step 2: Calculate the perimeter (trim needed)
To find perimeter, we need all three sides.
We know: base = 12 m, height = 8 m
Using Pythagorean theorem for the two equal sides:
Side = √(6² + 8²) = √(36 + 64) = √100 = 10 m
Perimeter = 10 + 10 + 12 = 32 m
Answer: You need 48 m² of roofing material and 32 m of trim.
A = ½ × b × h
Area = ½ × base × height
Units: square units (m², ft², etc.)
Key Point: The height must be perpendicular to the base!
P = a + b + c
Perimeter = side₁ + side₂ + side₃
Units: linear units (m, ft, etc.)
Key Point: Add all three sides together!
One angle is 90°
Height is one of the legs
Two equal sides
Height splits base in half
All sides different
Height must be measured
A triangular garden plot has a base of 15 meters and a height of 10 meters. Calculate the area and perimeter (assuming it's an isosceles triangle).
Your solution:
A triangular flag has sides of 5 cm, 12 cm, and 13 cm. Find the area and perimeter of the flag.
Your solution: