29+Area+of+a+Shaded+Region

Area of a Shaded Region:
By- Joey, John, and Drew

==Summary: The area of a shaded region is a difficult topic to grasp at first. The area of the darkened region subtracts the area of the unshaded region. Although it may be hard at first, with the help of our wiki page finding the area of the shaded region will come easy. Below are various, helpful lists of formulas, rules, properties, and important information. These lists are very important and it is vital for one to learn all the information on them. With this information success is almost eminent, but before perfection is gained it must be tested. That is why we have compiled three problems that will test and weigh your knowledge and solving skills on finding the area of a shaded region. ==

Rules/Steps to Finding the Area of a Shaded Region:
1. Identify all known shapes/figures 2. Find the area of the entire shape 3. Subtract the area of the unshaded region(s) from the area of the entire shape


 * Important Formulas:**

Area of a Trapezoid: 1/2(base1xbase2)xh Area of a Parallelogram: bxh Area of a Rhombus: bxh Area of a Kite: 1/2(diagonal1xdiagonal2)**
 * Area of a Circle: πr**2(//squared//)
 * Area of a Square: s**2(//squared//)
 * Area of a Rectangle: lxw


 * Directions: Find the area of the shaded region(s). Round to the nearest tenth when necessary.**


 * Examples:**

A= 10 x10 10 x10=100 in2(squared) Area of the Square= 100 in2(squared)
 * 1.**

A= π5 2(squared) π5 2(squared)= 78.5 in 2(squared) Area of the Circle= 78.5 in 2(squared)

100-78.5= 21.5 Area of the Shaded Region= 21.5 in 2(squared)

A= 40x20 (radius/width= 20) 40x20= 800 cm 2(squared) Area of the Rectangle= 800 cm 2(squared)
 * 2.**

A= π20 2(squared) π20 2(squared)= 1256.6 cm 2(squared) Area of the Circle= 1256.6 cm 2(squared)

1256.6÷2= 628.3 Area of the Semicircle= 628.3 cm 2(squared)

800-628.3= 171.7 Area of the Shaded Region= 171.7 cm 2(squared)


 * 3.

A= π12 2(squared) π12 2 (squared)= 452.4 Area of the Circle= 452.4 m 2(squared)

24= //x//√2 (45,45,90 Triangle) 24/√2= //x// 24/√2 x √2/√2 24√2/2= //x// 12√2= //x

A= 12√2 x 12√2 // 12√2 x 12√2= 288 Area of the Square= 288 m 2(squared)

452.4-288= 164.4 Area of the Shaded Region= 164.4 m 2(squared) **__Helpful Links__

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