Add Shapes
CONCEPTS
Types of Shapes
• The mixed shapes can be composed of 2 circles, 2 rectangles, a rectangle + a square, a rectangle + a triangle, or any other combination.
Problem Types
1) add the areas / volumes
2) add the perimeters
Circle Definitions
• Concentric: Concentric circles are 2 circles that have the same center, but a different radii.
• Tangent: A point of tangency is where a tangent line touches or intersects the circle
• Congruent: Congruent circles are circles that have the same radius but different centers.
PRACTICE PROBLEMS
Question 1 What is the area of the figure (see figure below)?
-- Answer -- 71
There are 2 rectangles inside the figure.
5 x 10 rectangle: 5 * 10 = 50
(12 – 5) x 3 rectangle: 7 * 3 = 21
Total area = 71
Question 2 Given the shape with equal side lengths. If the length of one side is 2, what is the area of the shape (see figure below)?
-- Answer -- 20
There are 5 total squares inside the figure.
A = l * w * 5 squares = 2 * 2 * 5 = 20
Question 3 What's the perimeter for the triangle on the right side of the figure (see figure below)?
-- Answer -- 37 + √130
There is a rectangle and a triangle.
Length of the hypotenuse: 9² + 7² = x², x = √130 (use Pythagorean theorem)
Perimeter = 8 + 10 + √130 + 19 = 37 + √130
Question 4 The track for a railroad goes around 2 circles that are tangent to one another. The 1st circle has a diameter of 30 feet and the 2nd circle has a diameter of 50 feet. What is the total distance the train travels?
-- Answer -- 80 π ft
Distance around 1st circle = 2πr = 2 π * 15 ft = 30 π ft
Distance around 2nd circle = 2πr = 2 π * 25 ft = 50 π ft
Total distance = 80 π ft
Question 5 What's the area of the shape (see figure below)?
-- Answer -- 28 + 9/2 π
A = Area rectangle + Area of half circle
A = 8 * 6 + 1/2 * π * 3² = 48 + 36 π
ACT PRACTICE PROBLEMS
