2Today we are going to review Area of a Triangle & Parallelogram. Then we are going to discover the Area of a Trapezoid.
3Watch carefully not to miss it! Area of a TriangleGiven the formula for area of a rectangle, we are going to use that information to discover the formula for the area of a triangle.Watch carefully not to miss it!
4Area of a TriangleGiven a right triangleMake a similar triangle,
5Given a right triangle Make a similar triangle, Area of a TriangleGiven a right triangleWhat polygon is this?A RectangleMake a similar triangle,and put both triangles next to each otherflip it
6We can use the formula for area of a rectangle Area of a TriangleWe can use the formula for area of a rectangleto find the formula for area of a triangle.Two triangles make one rectangle.We want to find half of the area of the rectangle.heighthbasebWhat is the formula for the area of a triangle?
7This holds true for any triangle Area of a TriangleThis holds true for any triangleheighthbase
8Area of a TriangleA triangle is half the area of a rectangle. To find the area of a triangle, you use the rectangle formula (base times height) and divide it in half.A = base • height213 m12 m5 mA = 5 • 12= 30 m22
9Area of a Triangle Area Perimeter Find the perimeter and area of this triangle.5 cm8 cmArea3 cm11 cmPerimeterP = a + b + cP =P = 24 cm
10Watch carefully not to miss it! Area of a TrapezoidGiven the formula for area of a triangle and the formula for area of a parallelogram we are going to use that information to discover the formula for the area of a trapezoidWatch carefully not to miss it!
11This trapezoid is regular. Area of a TrapezoidThis trapezoid is regular.regular trapezoidAlso known as an isosceles trapezoidThis trapezoid is an irregular trapezoid.irregular trapezoid
12Copy that trapezoid, flip it over, and put it next to the original Area of a Trapezoidb2b1hb1What polygon is it now?hhParallelogramb2(b1 + b2)Give the height,base 1 & base 2Copy that trapezoid, flip it over, and put it next to the original
13Area of a Trapezoid h (b1 + b2) put together with a similar flipped trapezoid, we found it made a parallelogram.Given our original trapezoidh(b1 + b2)We are going to use the area of a parallelogram to find the area of a trapezoid.Notice that the trapezoid is half the area of the parallelogram.It takes two trapezoids to make one parallelogram.
14Trapezoid Parallelogram Area of a Trapezoid h (b1 + b2) Notice that the trapezoid is half the area of the parallelogram.How do we find half the area?hHint: Think of area of a triangle.(b1 + b2)TrapezoidParallelogramA = (b1 + b2) • h2
15Area of Trapezoid Area of a Trapezoid 2 in 4 in A = (b1 + b2) • h 3 in
16Area of Trapezoid Area of a Trapezoid 3 m 5 m A = (b1 + b2) • h 4 m 2
17Area of a Trapezoid 5 in 4 in 6 in 7 in Here is another way to look at the trapezoid formula.Instead of dividing by 2, multiply by ½
18Take out your study guide! Area of a TrapezoidThe End!Take out your study guide!
19Area of a Trapezoid A = (b1 + b2) x h A = (4 + 5) x 3 2 A = (9) x 3 27 # 54 ftA = (base1 + base2) x height3 ft2A = (b1 + b2) x h5 ft2A = (4 + 5) x 32A = (9) x 327== 13.5 ft222
20Area of Polygons#6The Area of a figure is the number of square units needed to cover it.RectangleParallelogramTriangle748755108
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