An artist wants to cover in gold leaf a card with the initial letter H. Decompose the letter into simple shapes to find the area. How many centimeters will the artist need? Do not round your answer.

Question

The initial letter H is length is 6.0 on the sides, two 0.8 sides, and two 2.1 sides.

Answer 1

To find the area of the initial letter H, we can decompose it into simple shapes: two rectangles and one square.

The area of the square with sides of length 0.8 is:
Area = side x side
Area = 0.8 cm x 0.8 cm
Area = 0.64 cm²

The area of the rectangle with sides of length 2.1 and 0.8 is:
Area = length x width
Area = 2.1 cm x 0.8 cm
Area = 1.68 cm²

The area of the rectangle with sides of length 6.0 and 0.8 is:
Area = length x width
Area = 6.0 cm x 0.8 cm
Area = 4.8 cm²

Therefore, the total area of the initial letter H is:
Total area = 0.64 cm² + 1.68 cm² + 4.8 cm²
Total area = 7.12 cm²

So, the artist will need 7.12 square centimeters of gold leaf to cover the initial letter H.