area of quadrilaterals and triangles. what is a quadrilateral? any polygon with four sides and four...

Area of Quadrilaterals and Triangles

What is a quadrilateral?

•Any polygon with four sides and four vertices (or corners)

•All sides must be straight

Area of square, rectangle, and parallelogram•Area is a measure of the amount of space

contained inside a closed figure•The area of a square, rectangle, or

parallelogram is the product of its base and height:▫Area = base height

Find the area:

•A = b h•A = 11 5•A = 55 cm2

•A = b h•A = 6 4•A = 24 in2

• Which measurement is the base?

11cm• Which measurement

is the height? 5cm

The TRAPEZOID•The trapezoid is a quadrilateral with one

pair of parallel sides that are opposites▫The parallel sides are the “bases”▫The non-parallel sides are the “legs”▫The height is the distance between the

bases

Area of a Trapezoid•Since the bases are not the

same length, we have to take the average of them to find the area▫Average of bases = ½ (b1 + b2)

•Next, multiply the average of the bases by the height to get the area

Area of Trapezoid = ½ h(b1 + b2)

Find the area:

•Find the average of the bases▫½ (b1 + b2)▫½ (9 + 5)▫ = 7

•Multiply by the height▫6 7 = 42 in2

Triangles

•A triangle is half of a rectangle or half of a parallelogram

•If we know the area of a rectangle or parallelogram is base height, what could the are of a triangle be? Remember, a triangle is halfArea = ½

bh

Find the area

•Area = ½ bh•Area = ½ (108)•Area = ½80•Area = 40 mm2