Question

An artist wants to cover in gold leaf a card with the initial letter shown Decompose the letter into simple shapes to find the area. How many square c

letter:H 0.5 x 0.8, 6 x 0.8, 2.1 x ? how do I get to 10.65? show me step by step

Answer 1

To find the area of the letter H, we need to calculate the total area of each individual shape and then add them together.

The letter H can be decomposed into three rectangles:
1) The first rectangle has dimensions 0.5 x 0.8
2) The second rectangle has dimensions 6 x 0.8
3) The third rectangle has dimensions 2.1 x ?

Let's calculate the area of each rectangle:

1) Area of the first rectangle = 0.5 x 0.8 = 0.4 square units
2) Area of the second rectangle = 6 x 0.8 = 4.8 square units
3) Area of the third rectangle = 2.1 x ? = 2.1x square units

To find the missing dimension for the third rectangle, we can set up an equation:

0.4 + 4.8 + 2.1x = 10.65

Combine like terms:

5.2 + 2.1x = 10.65

Subtract 5.2 from both sides:

2.1x = 5.45

Divide by 2.1 on both sides:

x = 2.59

Therefore, the third rectangle has dimensions 2.1 x 2.59 and the total area of the letter H is 10.65 square units.