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
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.