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 cm 2 A = b  h A = 6  4 A = 24 in 2 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 (b 1 + b 2 ) Next, multiply the average of the bases by the height to get the area Area of Trapezoid = ½ h(b 1 + b 2 ) Area of Trapezoid = ½ h(b 1 + b 2 )

Find the area: Find the average of the bases ▫½ (b 1 + b 2 ) ▫½ (9 + 5) ▫ = 7 Multiply by the height ▫6  7 = 42 in 2

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 half Area = ½ b  h

Find the area Area = ½ b  h Area = ½ (10  8) Area = ½  80 Area = 40 mm 2