Presentation on theme: " Write down objective and homework in agenda Lay out homework (Graphing Picture) Homework(Area Review)"— Presentation transcript:
Write down objective and homework in agenda Lay out homework (Graphing Picture) Homework(Area Review)
A square room with an area of 324 square feet is tiled using square tiles with a side length of 1 foot. How many tiles line each wall of the room? A) 17 B) 18 C) 19 D) 20
Area: number of square units that it takes to cover the interior of a polygon, irregular figure, or circle Perimeter: distance measured around the sides of a polygon, you find the perimeter by adding all sides together area of a triangle: A=1/2 x b x h area of a rectangle: A= l x w area of a parallelogram: A = b x h area of a trapezoid: A = ½(b 1 + b 2 )h Square: a parallelogram with four right angles and four congruent sides Rectangle: a parallelogram with four right angles Parallelogram: a quadrilateral with both pairs of opposite sides parallel Trapezoid: a quadrilateral with exactly one pair of parallel sides Triangle: a polygon with three sides
Rhombus: a parallelogram with four congruent sides Circle: the set of all points in a plane that are equidistant from a given point, called the center Chord: a segment whose endpoints are on the circle Diameter: a chord that passes through the center of the circle Radius: a segment that has one endpoint at the center of the circle and the other endpoint on the circle Circumference: the distance around a circle. You calculate the circumference of a circle by multiplying the diameter by π
The perimeter of a polygon is the distance around the outside of the polygon. It’s equal to the sum of the lengths of the sides of the polygon. The area of a figure can be thought of as the space in the plane that the figure takes up.
To find the perimeter of a rectangle we need to know the length of its sides, l and w. Because opposite sides are equal we get the formula Perimeter = 2l + 2w ww l l
To find the area of a rectangle see how many unit squares will fit in it. The number of unit squares that will fit in the rectangle equals the area of the rectangle. Notice that the total number of unit squares that will fit in the rectangle equals the number of squares across times the number of squares down. This leads us to Area = length x width width length
What is the perimeter of this rectangle? l = 23 ft. w = 6 ft.
Perimeter = 2l + 2w = 2(23) + 2(6) = 46 + 12 = 58 ft. l = 23 ft. w = 6 ft.
What is the area of this rectangle? l = 23 ft. w = 6 ft.
l = 23 ft. w = 6 ft. Area = 23 x 6 = 138 sq. ft.
A square is a special type of rectangle with length = width. If we call the length of a side s then Perimeter = 4s Area = s 2
5 ft 11.5 ft. What is the perimeter of this triangle? 7 ft. 9.5 ft.
5 ft 11.5 ft. 7 ft. 9.5 ft. Perimeter = s 1 + s 2 + s 3 = 11.5 + 7 + 9.5 = 28.0 ft.
5 ft 11.5 ft. What is the area of this triangle? 7 ft. 9.5 ft.
5 ft 11.5 ft. Area = (1/2)(base)(height)= (1/2)(11.5)(5) = 28.75 sq. ft.
A trapezoid is a quadrilateral with 2 sides parallel. The two parallel sides are called the bases and are labeled B and b. B b
B b hh The area of the trapezoid is the sum of the areas of the two triangles. Area = (1/2)(B)(h) + (1/2)(b)(h) Factoring (1/2)(h) out of each term we get Area = (1/2)(h)(B + b)
What is the perimeter of this trapezoid? 18 in. 50 in. 20 in. 21 in.
18 in. 50 in. 20 in. 21 in. Perimeter = B + b + s1 + s2 = 50 + 20 + 21 + 21 = 112 in.
18 in. 50 in. 20 in. Area = (1/2)(h)(B + b) = (1/2)(18)(50 + 20) = 630 sq. in.
For any circle the circumference is always just over three times bigger than the diamter. The exact number is called π (pi). We use the symbol π because the number cannot be written exactly. π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)!
When we are doing calculations involving the value π we have to use an approximation for the value. Generally, we use the approximation 3.14 We can also use the π button on a calculator. When a calculation has lots of steps we write π as a symbol throughout and evaluate it at the end, if necessary.
For any circle, π = circumference diameter or, We can rearrange this to make a formula to find the circumference of a circle given its diameter. C = πd π = C d
Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 = 25.12 cm
Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 6 cm 13 cm Perimeter = 3.14 × 13 + 6 + 6 = 52.82 cm
We can find the area of a circle using the formula radius Area of a circle = πr 2 Area of a circle = π × r × r or
Use π = 3.14 to find the area of this circle. A = πr 2 4 cm = 3.14 × 4 × 4 = 50.24 cm 2
Use π = 3.14 to find the area of the following circles: A = πr 2 2 cm = 3.14 × 2 2 = 12.56 cm 2 A = πr 2 10 m = 3.14 × 5 2 = 78.5 m 2 A = πr 2 23 mm = 3.14 × 23 2 = 1661.06 mm 2 A = πr 2 78 cm = 3.14 × 39 2 = 4775.94 cm 2
Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm. 6 cm 13 cm Area of circle = 3.14 × 6.5 2 = 132.665 cm 2 Area of rectangle = 6 × 13 = 78 cm 2 Total area = 132.665 + 78 = 210.665 cm 2
6 inches 6 x 6 = 36 (area for the square) 3.14 x 3 2 = 28.26 36 – 28.26 = 7.74 inches
The square frame around the clock on Big Ben is a 7 meter square. What are the perimeter and area of the frame around the clock on the tower? P = 2L + 2W P = 28 meters A = lw A = 49 meters
Central Park in New York City is 2.5 miles long and 0.5 miles wide. What are the perimeter and area of Central Park? P = 2L + 2W P = 6 miles A = lw A= 1.25 miles
The Louvre in Paris has a pyramid that serves as the main entrance. Each face of the pyramid is 35 meters long and has a height of about 27.03 meters. What is the area of each face? A = 1/2bh A = 473.025
This building stands at the foot of Mt. Yatsugatake in Japan. It was designed to be an architect’s studio. If the base is about 6 meters long and 23.4 meters tall, what is the area of the face of the house facing you in this photograph? A = 140.4 meters
The windows of the Swiss Re building in London are rhombi. Each side length of the rhombi are approximately 5.7 ft. long. Given this length, what would be the perimeter of each rhombus? P=22.8 feet
Eye Bank is a medical facility in Venice, Italy. The trapezoid walls stand 12 meters high. The ground piece of the trapezoid is approximately 24 meters long and the top of the trapezoids are approximately 30 meters long. Given these dimensions, find the area of each trapezoid. A = 324 meters