Source: Cathedral of Maringá 02 2007 8712, Mariordo, Wikimedia Commons
Source: Cathedral of Maringá 02 2007 8712, Mariordo, Wikimedia Commons
The Cathedral of Maringá in Brazil is shaped like a large cone surrounded by triangle-shaped stained glass windows. There are 10 smaller triangles and 3 larger triangles.
If the height of each small triangle
is 20.5 meters and the base of each small triangle is 14.6 meters, what is the combined area of the smaller stained glass windows?
There are 10 small triangle stained glass windows.
The height of each window is 20.5 meters
and the base of each window is 14.6 meters.
Ryan's Plan
Each stained glass window is a triangle, so I will use the area formula for a triangle, A = 1 over 2 1 2 bh, to calculate the area of one window. Once I know the area of one window, I can multiply that area by 10 to get the area of all 10 smaller stained glass windows.
Use the area formula for a triangle, A = 1 over 2 1 2 bh,
since each stained glass window is in the shape of a triangle.
Write an equation that you could use to calculate the area of one stained glass window.
A = 1 over 2 1 2 (14.6 m)(20.5 m)
Area of one window:
A = 1 over 2 1 2 (14.6 m)(20.5 m)
= 149.65 m2
Area of 10 windows:
A = (10)(149.65 m2)
= 1496.5 m2
Strategy check: Use compatible numbers to estimate your answer. Estimate 14.6 meters and 20.5 meters to the nearest five meters.
14.6 meters → 15 meters
20.5 meters → 20 meters
Area of one window: A = 1 over 2 1 2 (15 m)(20 m) = 150 m2
Area of 10 windows: A ≈ 10(150 m2) = 1,500 m2
The estimate of 1,500 m2 is close to the actual answer of
1496.5 m2, so the answer is reasonable.