Unit 4 Homework Triangles, Rectangles, Trapezoids (perimeter, area) Friday Sept 23 rd Circles (Area, Perimeter) Monday Sept 26 th Volume of Prisms and

Unit 4 HomeworkUnit 4 HomeworkTriangles, Rectangles, Trapezoids (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





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



Height

Base

A = ½ bh

P = s1 + s2 + s3

A = P =A = P =A = P =

A = P =A = P =A =



12.3 in

16 ft

413

9

Parallelograms: •Opposite sides are parallel and congruent

***If the angles are right, then it becomes a rectangle!



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)



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



Average the bases

A =

A =

A =

P =

P =





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

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)


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 =


5 cm

Directions: Find the area of the shaded region. Use 3.14 for π


Directions: Find the area of the shaded region. Leave answer in terms of π

2 in


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.


Can you identify the base?

V = B h V = BhV = l*w*h V = (πr2)h


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



V = 4/3 πr3

14

Find the volume. Use 3.14, 22/7, and also leave in terms of π.

V = V = V =


Hemisphere: Half of a sphere.

V = 4/3 πr3 ÷ 2

V = 4/6 πr3

V = 2/3 πr3

Find the Volume:


Documents

Unit 4 Homework Triangles, Rectangles, Trapezoids (perimeter, area) Friday Sept 23 rd Circles (Area, Perimeter) Monday Sept 26 th Volume of Prisms and