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Unit 4 HomeworkUnit 4 HomeworkTriangles, Rectangles, Trapezoids, Parallelograms (perimeter, area) •Friday Sept 23rd
Circles (Area, Perimeter)•Monday Sept 26th
Volume of Prisms and Cylinder (vocabulary terms)•Tuesday Sept 27th
Volume of Cone, Pyramids, Sphere (vocabulary terms)•Wednesday Sept 28th
Test Friday Sept 30th
Rectangles: A polygon such that…•Opposite sides are equal length•4 right angles
Squares: A polygon such that…•All four sides are congruent (opposite sides parallel) •4 right angles
***Squares are special case of rectangle! All square are rectangles.
***But not all rectangles are squares. Only SOME rectangles are squares.
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Rectangles: Squares:
A = lw P = l+w+l+w A = s * s P = s + s + s + s or A = s2 P = 4sA = bh P = 2l + 2w
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Classifying Triangles:
By Sides… By Angles…
Equilateral-All sides Acute- All angles less 90equal length
Isosceles- 2 sides equal Obtuse- 1 angle bigger 90length
Scalene- No sides equal Right- 1 angle = 90length
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Height
Base
A = ½ bh
P = s1 + s2 + s3
A = P =A = P =A = P =
A = P =A = P =A =
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
12.3 in
16 ft
413
9
Parallelograms: •Opposite sides are parallel and congruent
***If the angles are right, then it becomes a rectangle!
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Therefore for a parallelogram……..A = bh
P = s1 + s2 + s3 + s4
Trapezoids: A shape with exactly one set of parallel lines
b1 b1
b2b2
HeightHeight
The bases of a trapezoid are different lengths. (If they were equal, this would make both sets of opposite sides parallel, which is not the definition of a trapezoid)
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
But what if you COULD make the two bases equal to each other? Then the trapezoid would become a rectangle, and we could use the formula A = lw
Trapezoid Area:
A = ½ h(b1 + b2) or )2
( 21 bbh
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Average the bases
A =
A =
A =
P =
P =
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
A pool is 8 ft by 12 feet. There is a 5 foot cement sidewalk around the pool. What is the area of the cement sidewalk?
812
Triangles, Rectangles, Parallelograms, Trapezoids
(Area and Perimeter)
Area and Perimeter Formulas:
Triangle: A = ½ bh P = Rectangle: A = bh P = 2l + 2wSquare: A = s2 P = 4lParallelogram: A = bh P = 2l + 2wTrapezoid: A = ½ h(b1 + b2) P = Circle: A = πr2 C = 2πr or C = πd
s1 + s2 + s3
s1 + s2 + s3+s4
Circles (Area and Perimeter)
Radius Diameter
(Circumference means Perimeter)A = πr2 C = 2πr or C = πd
Circle: All points equal distant from a given point (2-D)
Circles (Area and Perimeter)
A = C =
A = C =
A = C =
Find Area and Perimeter. Use 3.14 for π.
Find Area and Perimeter. Use for π.7
22
28 cm
5.2 in
A = C =
A = C =
A = C =
Directions: Find the Area and Perimeter. Leave answer in terms of π
18 mm
A = C =
A = C =
A = C =
Circles (Area and Perimeter)
5 cm
Directions: Find the area of the shaded region. Use 3.14 for π
Circles (Area and Perimeter)
Directions: Find the area of the shaded region. Leave answer in terms of π
2 in
Circles (Area and Perimeter)
Volume of Prisms and Cylinders
Volume is a the space an object takes up. It is three dimensional (length x width x height). Therefore, the label is always cm3, in3, m3, etc.
A prism is a 3-D figure that has a polygon for a base, and the height of the prism is an extension of that base.
A cylinder is not a prism (because the base is a circle…which is not a polygon). But cylinders are similar to prisms because the height is an extension of the base.
Volume of Prisms and Cylinders
Can you identify the base?
V = B h V = BhV = l*w*h V = (πr2)h
Volume of Prisms and Cylinders
Which has more volume?
Volume of Cones, Pyramids, Spheres, Hemipsheres
Cone: Has a circle base, meets up at a point.
Pyramid: Has a polygon for a base (usually a square or a triangle, but can be any polygon).
Sphere: All points equal distant from a given point (in 3-dimensions)
Cones and Pyramids are 1/3 of a prism
Cone: V = 1/3 BhV = 1/3 (πr2)h
Triangle-based: V = 1/3 Bh V = 1/3 (1/2 bh)h
Rectangle-Based: V = 1/3 BhV = 1/3 (lw)h
Volume of Cones, Pyramids, Spheres, Hemipsheres
Volume of Cones, Pyramids, Spheres, Hemipsheres
V = 4/3 πr3
14
Find the volume. Use 3.14, 22/7, and also leave in terms of π.
V = V = V =
Volume of Cones, Pyramids, Spheres, Hemipsheres
Hemisphere: Half of a sphere.
V = 4/3 πr3 ÷ 2
V = 4/6 πr3
V = 2/3 πr3
Find the Volume:
Volume of Cones, Pyramids, Spheres, Hemipsheres
