6/06/2010 @ 2:07 PM

Measurement

In this unit, you will learn about the pythagorean theorem and the perimeter/area/surface area/volume of shapes and 3-D objects. First, there is the pythagorean theorem.

The equation for the pythagorean theorem is a² + b² = c²

c

^{² is the hypotenuse side.}

^{ }

EXAMPLE: Side a = 2 Side b = 8

What is the measure of side c?

a² + b² = c²

(2)² + (8)² = c²

4 + 64 = c²

68 = c²

68 squared = c² squared

8.2 = c

Another thing we learned about is perimeter and area.

Here are the equations:

**Rectangle**

__Perimeter:__P= l + l + w + w OR P = 2 (l + w)

__Area:__A = lw

**Parallelogram**

__Perimeter:__P = b + b + c + c OR P = 2 (b + c)

__Area:__A = bh

**Triangle**

__Perimeter:__P = a + b + c

__Area:__A = bh/2 OR 1/2bh

**Trapezoid**

__Perimeter:__P = a + b + c + d

__Area:__A = (a + b)h /2 OR 1/2 (a + b)h

**Circle**

__Circumference:__C = πd OR 2πr

__Area:__A = πr²

**Cylinder**

__Surface Area:__SA=2πr²+2πrh

__Volume:__V=πr²h

**Sphere**

__Surface Area:__SA=4πr²

__Volume:__V=4/3 πr³

**Cone**

__Surface Area:__SA=πrs+πr²

__Volume:__V=1/3 πr²h

**Square base pyramid**

__Area:__A=2bs+b²

__Volume:__V=1/3 b²h

**Rectangular prism**

__Area:__A=2(wh+lw+lh)

__Volume:__V=lhw

**Triangular prism**

__Area:__A=ah+bh+ch+bl

__Volume:__V=1/2 blh

PRACTICE:

1)

What is the perimeter of this triangle?

ANSWER: P = 9 + 5 + 11

P = 25

2) What is the area of a rectangle that has a length of 12m and a width of 4m?

ANSWER: A = lw

A = (12) (4)

A = 48m

3) Soda is sold in aluminum cans that measure 15cm in height and 6cm in diameter. What is the volume?

ANSWER: V=πr²h

V = (3.14)3² (15)

V = (3.14)9 (15)

V = 423.9 cm³

4)

Find the volume of this triangular prism.

V=1/2 blh

V= 1/2 (6.2) (4.3) (8.5)

V= 1/2 (226.61)

V= 113.30cm³

Another thing we learned about is the angle relationships in triangles.

The sum of the interior angles in a triangle is 180 degrees. Therefore, a + b + c = 180 degrees.

The sum of the exterior angles of a triangle is 360 degrees. Therefore, x + y + z = 360 degrees.

The exterior angle of each v ertex is equal to the sum of the two opposite interior angles, so x = b + c, y = a + c, and z = a + b. EAT (Exterior angle theorem)

A midpoint is a point that divides a line in half EQUALLY.

*TIP: the formula for the sum of the interior angles of a regular polygon is 180 (n-2)*

In any quadrilateral, when you connect the midpoints of the sides, a parallelogram/rhombus is formed.

Labels: Lessons

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