3.1b: Area and Perimeter
M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three
M(G&M)–10–7 Uses units of measure appropriately and consistently when solving problems across content strands; makes conversions within or across systems and makes decisions concerning an appropriate degree of accuracy in problem situations involving measurement in other GSEs. (State)
- Quadrilaterals and composite shapes
Area of Parallelograms
Base (b) = One side of the parallelogram
Height (h) = distance between the bases (must be perpendicular)
Base
Base
height
Area of a Parallelogram = (b)(h)
Why ?
Base
Base
height
What shape will it make when we cut off the triangle on the side and put in on the other side?
A rectangle with the area= (base)*(height)
Area if Triangles
bhA2
1
*b= base of the triangle
*h = height of the triangle
* Both are touching the 90 degree angle in the triangle
But Why ?
Example
A rhombus has an area of 50 square mm. If one diagonal has a length of 10 mm,How long is the other diagonal.
Area of a Trapezoid
)(2
121 bbhA
bases) ebetween th distance (the heighthBase (parallel side)
Base
Height (has to be perpendicular to bases)
side parallel (opposite baseother theb
side) parallel (a bases theof one
2)
1
b
M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope.
Find the area
Use a geometric (area) approach Instead of algebraic (slope, distance)
Now you have a rectangle With dimensions of 4 by 6.
2
rectangle units 24)6)(4( Area4 units
6 units
To get the area of the original triangle, subtract the new triangles from the overall rectangle. This will leave you with the area of the original triangle.
1
23
2
3
2
2
2
1
u 4)4)(2(2
1
u 6)6)(2(2
1
u 4)4)(2(2
1
A
A
A
2
s trianglerectangleTriangle Original
u 10
14 - 24
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