Question

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?

Answer 1

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

Explanation:

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