Area of Quadrilaterals

Objectives

• I can find the areas of parallelograms, rhombuses, and trapezoids.

Area of a Parallelogram

• What is a parallelogram?• -a quadrilateral in which opposite sides are

parallel and congruent.

How do we find the area of a parallelogram?

• In front of you is a parallelogram on the paper.

• Cut it out• Cut your parallelogram along the dotted line.• Now move your triangular piece to the other

side of the parallelogram.

• What figure have you formed?• Rectangle• Does it have the same area as the

parallelogram?• Base of the parallelogram is equal to• The length of a rectangle• The height of the parallelogram is equal to• The width of a rectangle

Area of parallelogram continued

• Area of parallelogram is equal to• Area of rectangle• How do we find the area of a rectangle?• Area = product of the length and width• Area = length times width• A=(l)(w)• How do we find the area of a parallelogram?• Area = the product of the base and height• Area = base time height• A = bh

Find the area !

• The base of my parallelogram is 13 inches and the height is 9 inches. Find the area.

• A = bh• A = 13 · 9• 117 inches squares• Why are the units squared?• We are multiplying and inch by an inch. This is

no different than multiplying 2 time 2 which can be written as 2²

Math Talk

• On a piece of paper answer the following:• How is the relationship between the length

and width of a rectangle similar to the relationship between the base and height of a parallelogram?

Trapezoid• What is a trapezoid?• A quadrilateral in which two sides are parallel.

Finding the area of a trapezoid• Look at the two congruent trapezoids. What

do you notice?• You should notice that the two trapezoids can

fit together to form a parallelogram.

• How does the trapezoid compare to the parallelogram?

• It is half of it.

• If the trapezoid is half the parallelogram, then the area of the trapezoid is?

• Half the parallelogram• The height of the parallelogram is the same as

the height of the trapezoid. The base of the parallelogram is the sum of the two bases of the trapezoid.

• The Area of the trapezoid is found by adding base 1 and base 2 and multiplying it by ½ the height

• Area of a Trapezoid = 1/2h(b₁ +b₂)

Try some!

• A section of deck is in the shape of a trapezoid, what is the area of this section of deck if base one is 15 feet, base 2 is 25 feet and the height is 21 feet.

• Area of a Trapezoid = 1/2h(b₁ +b₂)• Area = ½ · 21 (15 + 25)• 420 ft²

Math Talk

• On your piece of paper. Answer the following.• Does it matter which of the trapezoids bases is

substituted for b₁ and which is substituted for b₂? Why or Why not?

Rhombus

• A rhombus is a quadrilateral in which all sides are congruent and opposite sides are parallel.

• Can a square be classified as a rhombus?• Yes, all side are congruent and opposite side

are parallel.• Some people call a rhombus a • Diamond or a kite• A diagonal is a line that can be drawn from

one vertices to the opposite vertices.

Area of a rhombus• A rhombus can be divided into four triangles.• Go ahead and cut your rhombus into 4

triangles.• Rearrange them into another shape.• Rectangle• The base of the rectangle is the same length

as one of the diagonals of the rhombus. The height of the rectangle is ½ the length of the other diagonal.

Rhombus Formula

• The area of a rhombus is half of the product of its two diagonals.

• A = 1/2·d₁ · d₂

Try one!

• Cedric is constructing a kite in the shape of a rhombus. The spars (wood pieces that fabric attaches to. These would be the diagonals) of the kite measure 15 inches and 24 inches.

• How much fabric will Cedric need for the kite?• A = 1/2d₁d₂• A= ½ · 15 · 24• A= 180 in²

Looking at the formulas

• What were all the formulas based upon?• The parallelogram or rectangle.

Higher Order Thinking

• Answer the following:• Simon says that to find the area of a trapezoid,

you can multiply the height by the top base and by the bottom base, then add the two products together and divide the sum by 2. Is Simon correct? Explain your answer.

Advanced Multistep

• The height of a trapezoid is 8 in. and its area is 96 in². One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases. Explain how you found your answer.

Multistep

• The height of a trapezoid is 8 in. and its area is 96 in². One base of the trapezoid is 6 inches long. What is the length of the other base. Explain how you found your answer.

Practice