Presentation on theme: "Parallelograms, Triangles, and Circles 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into."— Presentation transcript:
6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems
Students will be able to: Find the areas of parallelograms, triangles, and circles Find the circumference of circles Find the area of complex figures
AREAS OF POLYGONS QUICK REVIEW: What is the formula to find the area of a rectangle? A = l x w
AREA OF A PARALLELOGRAM h b Let’s Discover the formula for a parallelogram!
AREA OF A PARALLELOGRAM To do this let’s cut the left triangle and… h b
The circumference of a circle is The distance around a circle Hint: Circumference remember circle around
Diameter Radius centre What is the formula relating the circumference to the diameter?
People knew that the circumference is about 3 times the diameter but they wanted to find out exactly. C = ? x d C ≈ 3 x d This means APPROXIMATELY EQUAL TO
Egyptian Scribe Ahmes. in 1650 B.C. said C≈3.16049 x d ArchimedesArchimedes, said C ≈3.1419 x d Fibonacci. In 1220 A.D. said C≈3.1418xd What is the value of the number that multiplies the diameter to give the circumference????
8 mm A = (3.14)( 8 2 ) A =(3.14)(64) A = 200.96 mm 2
13 cm If you are given a diameter, divide it in half to find the radius. 13 divided by 2 equals 6.5 cm. A = (3.14)(6.5 2 ) A = (3.14)(42.25) A = 132.665 cm 2
A circle is defined by its diameter or radius Diameter radius The perimeter or circumference of a circle is the distance around the outside The area of a circle is the space inside it The ratio of π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14 The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula A=πr 2
Finding circumference Naming the parts of a circle Finding the area of circles
Use the appropriate formula to find the area of each piece. Add the areas together for the total area.
|27 cm | 10 cm 24 cm Split the shape into a rectangle and triangle. The rectangle is 24cm long and 10 cm wide. The triangle has a base of 3 cm and a height of 10 cm.
Rectangle A = lw A = 24(10) A = 240 cm 2 Triangle A = ½ bh A = ½ (3)(10) A = ½ (30) A = 15 cm 2 Total Figure A = A 1 + A 2 A = 240 + 15 = 255 cm 2
Try This Area of Parallelograms Game- You have to be QUICK!!This Area of Parallelograms Game Try This Baseball Game that finds area of trianglesThis Baseball Game Homework: Reteaching/Practice 9.4 HO