SPRINGBOARD UNIT 5 GEOMETRY 5.1 Area and Perimeter Perimeter the distance around an object. To find perimeter, add all sides. Area the amount of space inside a 2 dimensional object. Measurements for area are to the power of two. To find area, use the correct formula for each shape. Composite Shapes composed of 2 or more simple shapes. To find area of composite shapes, divide the shape into shapes you know and add areas of the shapes to find total area. Find the area and perimeter of the following rectangle. A=4x3 A=12m 2 Perimeter= 3+3+4+4=14m (Remember that opposite sides of a rectangle are equal.) 5 To find perimeter, find missing sides lengths. Missing side lengths are in RED. 3 A Perimeter 5+3+3+7+8+10= 36 units To find area, divide shapes into simple shapes. The red dotted line shows how it was divided. B Rectangle A A=5x3 A=15 units 2 Rectangle B A=8x7 A=56 units 2 Add the 2 areas together= 15+56=71 units 2 Click for live video tutorial: Definitions of Perimeter and area: http://www.khanacademy.org/math/geometry Area and perimeter of rectangles: http://www.khanacademy.org/math/geometry/basicgeometry/v/area and perimeter
5.2 Investigating is the ratio of the circumference to the diameter. For 22 use 3.14 or. 7 Radius the distance from the center to the outside edge of a circle. Diameter the distance across the circle going through the center. Circumference the distance around the circle. Find the circumference. C= d C= 3.14x10 C= 31.4 in Find the circumference. Since you were given the radius, find the diameter first. If the radius is 6mm, then diameter is 12mm. C= d C= 3.14x12 C= 37.68 mm Click for live video tutorial: http://www.khanacademy.org/math/geometry/circles topic/v/circles radius diameter andcircumference
5.3 Area of Polygons and Circles Find the area of the parallelogram. A=7x3 A=21in 2 Find the area of the triangle. 1 A= bh 2 1 A= x15x12 2 1 A= x180 2 A=90cm 2 Find the area of the trapezoid. A= 2 1 h(b 1 +b 2 ) A= 2 1 x8x(12+15.4) A= 2 1 x8x27.4 A=4x27.4 A=109.6 cm 2 Continue
5.3 Area of Polygons and Circles Continued. Missing dimensions of shapes are also addressed even though the information is not covered in book. To find missing dimensions, fill in the information you know and solve for what you do not know. Find the base of a parallelogram if its height is 9 feet and its area is 27 square feet. 27=b9 9 9 3 ft=b Find the missing dimension of a triangle with a height of 12 inches and an area of 24 inches squared. A= 2 1 bh 24= 2 1 b12 24=6b 6 6 4in=b Click for interactive practice: Area of parallelogram: http://www.mathsisfun.com/geometry/parallelogram.html Area of triangle: http://www.mathsisfun.com/algebra/trig area triangle without rightangle.html
Find the area of the circle. For the formula for area of a circle, you need the radius. Since the diameter is 14 inches, the radius is 7 inches. A= r 2 A= 3.14 x 7 2 A= 3.14 x 49 A=153.86 inches 2 Find the area of the semicircle. Find the area of the full circle first. A= r 2 A=3.14 x 5.5 2 A=3.14 x 30.25 A=94.985 yd 2 Since this is a semicircle, you must cut the area in half. 94.985 yd 2 2 = 47.493 yd 2 Find the diameter of a circle with a circumference of 109.9 meters. C= d 109.9=3.14d 3.14 3.14 35m=d Click for live video tutorial: http://www.khanacademy.org/math/geometry/circles topic/v/area of a circle
NOTE: Sections 5.4 through 5.6 are not covered in 6 th grade curriculum. 5.7 Symmetry and Transformations Line of Symmetry a line that cuts a figure in half creating a mirror image. Transformations movement of a figure on a coordinate plane. Types of Transformations: Reflection to flip an object on a coordinate plane Translation to slide and object on a coordinate plane Rotation to turn an object on a coordinate plane Draw all lines of symmetry on the figures below. Graph the following points on a coordinate plane. (3,4) Starting at (0,0), move 3 right and 4 up. (1, 2) Starting at (0,0), move 1 right and 2 down. ( 2,1) Starting at (0,0), move 2 left and 1 up. ( 4, 2) Staring at (0,0), move 4 left and 2 down. Click for live video tutorial: Coordinate plane: http://www.khanacademy.org/math/algebra/ck12 algebra 1/v/thecoordinate plane
5.7 Symmetry and Transformations Continued.. Graph points D( 3,4), E( 1,3) and F( 2,0). Then connect the points DEF to form a triangle. Translate triangle DEF 4 units to the right and 3 units down. Give the new coordinates of triangle D E F. To translate triangle DEF, move each point 4 units right and 3 units down. Then connect the points to form triangle D E F. The new coordinates for triangle D E F are D (1,1), E (3,0), (2, 3). Graph points G(4, 1), H(2, 2), and J(3, 5) to form triangle GHJ. Draw a reflection of triangle GHJ over the x axis to form triangle G H J and give the coordinates. The draw a reflection of triangle GHJ over the y axis to form G H J and give the coordinates. To reflect triangle GHJ over the x axis, take each point and reflect it the opposite direction from the x axis. Point G is 1 down from the x axis, so reflect it 1 up. Point H is 2 down from the x axis, so reflect it 2 up. Point J is 5 down from the x axis, so reflect it 5 up. Connect the points to form triangle G H J. The new points are located at G (4,1), H (2,2), and J (3,5). To reflect triangle GHJ over the y axis, take each point and reflect it the opposite direction from the y axis. Point G is 4 right from the y axis, so reflect it 4 left. Point H is 2 right from the y axis, so reflect it 2 left. Point J is 3 right from the y axis, so reflect it 3 left. Connect the points to form triangle G H J. The new points are located at G ( 4, 1), H ( 2, 2), and J ( 3, 5). Click for tutorial and interactive practice: http://www.mathsisfun.com/geometry/transformations.html
5.8 Exploring Volume Volume the amount of space inside a 3 dimensional object. Measurements for volume are to the power of three. Find the volume of a rectangular prism that has a height of 7 centimeters, a base of 6 centimeters, and a width of 5 centimeters. V=bwh V=6x5x7 V=30x7 V=210 cm 3 Find the missing dimension of the rectangular prism. V=bwh 189=9w7 189=63w 63 63 3 yd=w Click for tutorial and interactive practice: http://www.mathsisfun.com/cuboid.html