Answer:
Approximately 21 inches of lead are needed to seal the edges of one sun catcher. If the craftsperson has two 3-foot lengths of lead, 3 sun catchers can be sealed.
Step-by-step explanation:
The diagram of the sun catcher appears to make four right triangles, two of equal size on the top and two equal size on the bottom. Since the base and height (legs) of each triangle are given, we can use the Pythagorean Theorem to find the missing side (hypotenuse) using the following formula:
a² + b² = c², where 'a' and 'b' are the legs and 'c' is the hypotenuse
For the two top triangles a and b are both 2.75:
2.75² + 2.75² = c² or 15.125 = c² take the square root: √15.125 = √c²
c = 3.89 inches
For the bottom two triangles a = 2.75 and b = 5.5:
2.75² + 5.5² = c² or 37.8125 = c² take the square root: √37.8125 = √c²
c = 6.15 inches
For each sun catcher, you need to add all four sides of the triangles:
(2)(6.15) + (2)(3.89) ≈ 20.1 inches
With two 3 foot lengths of lead:
2 x 3 = 6 foot x 12 inches/foot = 72 inches
Total divided by the number needed per sun catcher:
72 ÷ 20.01 = 3.6, or 3 complete sun catchers
