Use Area to Solve Problems Practice
An artist wants to cover in gold leaf a car with the initial shown. Decompose the letter into simple shapes to find the area. How many square centimeters of gold leaf will the artist need? Do not round your answer.
(1 point)
To find the area of the letter "C" decomposed into simple shapes, we can see that it is made up of a rectangle and two semicircles.
The rectangle can be divided into two smaller rectangles:
- The width of the rectangle is 2 cm
- The height of the rectangle is 6 cm
So, the area of the rectangle is 2 cm x 6 cm = 12 square cm
The two semicircles can be combined to form a full circle:
- The diameter of the circle is 6 cm, so the radius is 3 cm
Using the formula for the area of a circle (A = πr^2):
A = π(3 cm)^2
A = π(9 cm)
A = 9π square cm
Adding the areas of the rectangle and the circle together:
12 square cm + 9π square cm ≈ 40.28 square cm
Therefore, the artist will need approximately 40.28 square centimeters of gold leaf to cover the letter "C" on the car.