A church door is in the shape of a rectangle with a semi-circular arch. The rectangular part is 2m high and the door is 90cm wide. What is the distance around the whole door?

Question

Maverick Smith · Accepted Answer

#490+45pi cm=490+45(3.14)~=631.4# cm

We have a door that is rectangular with an arch on the top. What's the perimeter? Let's do the rectangular part first: The bottom of the door is the 90cm width. The sides of the door are the 2m height, or 200cm each. So we're at #2(200)+90=490cm# for the sides so far. Now to the top of the door and the arch. The circumference of a circle is #C=2pir# and since we only need half that, it's #pir#. The radius is half the width of the door, so 45cm, which gives us the circumference of the arch #=45pi# cm. We can add that to what we already have and get: #490+45pi# cm We can approximate #pi# to be #3.14# and so get: #490+45pi=490+45(3.14)~=631.4# cm

Allison Allen · Answer

undefined To find the distance around the whole door, you calculate the perimeter of the rectangular part and add it to the circumference of the semi-circle.

The perimeter of the rectangle = 2*(height + width)
                                 = 2*(2m + 0.9m)
                                 = 2*(2.9m)
                                 = 5.8m

The circumference of the semi-circle = π*r, where r is the radius of the semi-circle. Since the width of the rectangle is the same as the diameter of the semi-circle, the radius is half of the width.
                                      = π*(0.9m/2)
                                      = π*(0.45m)
                                      ≈ 1.41m (approximated to two decimal places)

The total distance around the whole door = Perimeter of rectangle + Circumference of semi-circle
                                         = 5.8m + 1.41m
                                         ≈ 7.21m (approximated to two decimal places)

So, the distance around the whole door is approximately 7.21 meters.