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6.7 Areas of Triangles and Quadrilaterals

The area of a Square Area of a Square

Postulate If two polygons are congruent, then they have the same area.

Area Addition Postulate
The area of a region is the sum of the area of it nonoverlapping parts. The Blue area is Area of A+B+C+D+E+F+G+H

The Area of a Rectangle Area of a Rectangle is Base times height.

The Area of a Parallelogram
is Base times height.

Area of a Triangle Area is one half base times height, even if the height is outside of the triangle

Area of a Trapezoid Area is one half height times(base1 + base2).
Height is from base1 to base2

Area of a Kite Area is one half of diagonal1times diagonal2

Area of a Rhombus Area is one half of diagonal1 times diagonal2

Find the Area Square

Find the Area Square Area in2

Find the Area Rectangles Area =

Find the Area Rectangles Area = 27.36in in2 = in2

Find the Area Parallelogram Area =

Find the Area Parallelogram Area = in2

Find the Area Find the area of the Trapezoid

Find the Area Find the area of the Trapezoid height = 4 base1 = 4

Find the Area Find the area of the Trapezoid Area height = 4 ½(4)(4+6)
½(4)(10) base1 = 4 2(10) base2 = 6 Area = 20

Find the length of the diagonal
Rhombus Area is 192 units2

Find the length of the diagonal
Rhombus Area is 192 units2 192 = ½(8+16)(diagonal) 192 = ½(24)(diagonal) 192 = 12(diagonal) 16 = diagonal What is x ?

Find the Area What is the total Area

Find the Area What is the total Area Trap = ½(3)(10+16) = 39
Rect. = 8(16) = 128 Total = 167in2

Homework Page 376 – 377 # 14 – 38

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