BYU Geometry Unit 1:Perimeter and Area

How would you calculate the area of a parallelogram(formulas)?

-A=bh -A=1/2(diagonal1)(diagonal2)

perimeter of a polygon

-Sum of the length of its sides -quadrilateral(square/rectangle): P=2l+2w

Define the height and base of a paralleogram

-height(h): the distance between the parallel sides -base(b): the parallel sides

area of a polygon

-measure of the region inside the polygon -square units:# of squares of a particular size to cover a region -quadrilateral(square/rectangle):A=lw

How do you find the area of a trapezoid? (think about it as two triangles)

A= area of triangle 1+ area of triangle 1 A=1/2bh+1/2bh *A=1/2h(b+b)*

Formula for the area of 1/4 of a rhombus (aka another way to find area of a triangle):

A=1/2(diagonal/2)(diagonal/2) *A=1/8(diagonal)(diagonal) *

Formula for the area of a triangle:

A=1/2bh

Formula for the area of a rhombus(using triangles):

A=4(1/8)(diagonal)(diagonal) *A=1/2(diagonal)(diagonal)*

how would you find the area of a regular polygon using apothems?

A=n(1/2sa)=1/2(nsa)

How would you calculate the area of a triangle using their side lengths aka Heron's formula? (a,b,c=side lengths)

S=1/2(a+b+c) A=√s(s-a)(s-b)(s-c)

If a parallelogram has the same length/base and width/height of a rectangle, what else would they have in common?

They would have the same *area*

Define a trapezoid

a quadrilateral with one pair of parallel sides

define apothem

a segment from the center of a regular polygon perpendicular to a side

T44: If one side of a triangle is longer than a second side, then the measure of the angle opposite the first side is _______ than the measure of the angle opposite the second side.

greater -Angles correspond to their sides

T50:The perimeters of __________ polygons are __________ to corresponding sides

similar, proportional

T51: The areas of _______ polygons are _________ to the __________ or the ratio of corresponding sides.

similar, proportional, square

T43: In a triangle, the sum of the lengths of any ______ sides is always _______ than the length of the third side.

two, greater