area of triangles and quadrilaterals basic equations and applying to irregular polygons

Area of Triangles and Quadrilaterals

Basic equations and applying to irregular polygons

Triangles

Half the area of the Rectangle or parallelogram it would fit intoHeight or Altitude – perpendicular segment from vertex to side opposite, could be outside the triangle

Rectangles and Parallelograms

These two go together because the are very similar shapesBase time heightRemember the height is the perpendicular segment between two basesRectangle – sides are perpendicularParallelogram – need to have height or calculate the height, may be outside the parallelogram

Trapezoid

Think of this as two triangles – they have different basesSum of two bases times height divided by 2

Can’t always divide trapezoid into a rectangle and two triangles, the end triangles may not be the same

221 hbb

Kite

Split into 2 congruent triangles using the diagonalsArea of one triangle times 2

2

2*1 diagdiag

2

2*12

halfdiagdiag

Example

Find the area of the large rectangles and subtract the missing corner

Divide shaded region into 2 rectanglesFind the area of each rectangle and addThem together

Example

Given the area find the base of the triangleSub in what you know into the areaEquation for a triangle and solve for b

y

5

6

9

15

6x

Dotted lines represent heights of the same triangle but from different views.Look at the three triangles, they should all have the same area, set up area equation and solve for x and y

Homework

All Homework Due WednesdayPg 425 1-9 odd, 17 and 20Honors 21-24Pg 430 1-11 oddHonors 18 and 19