Areas of Triangles, Trapezoids, and

Rhombi

Objective: TLW find the areas of triangles, trapezoids, and rhombi. SOL G.10

What does the area of a triangle have in common

with the area of a rectangle or a parallelogram?

Let’s look at a Triangle Looking at the triangle

below, how can you relate this image to a rectangle?

What if we drew a line perpendicular to AC through point A? through point C? What does this do for us?

Let’s look at a Triangle

Could we follow this with an additional step? What would that step be?

How can we use this diagram and the information we now have to create the formula for area of a triangle?

The Area of a Triangle:

If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then: A = (1/2) b h Where b = base; h = height

Let’s Try One!!!!

A = (1/2) (7.3 cm)(3.4 cm) = (1/2) (24.82 cm2) = 12.41 cm2

How can we take this formula for the area of a

triangle and apply it to the formula for a trapezoid?

Let’s look at a Trapezoid

Could we create a trapezoid from triangles? If so, how?

h

b1

b2

Area of Trapezoid WXZY: = area of Δ WYX + area of Δ YZX = (1/2) (b1 )(h) + (1/2) (b2 )(h) = (1/2) (b1 + b2 ) h

= (1/2) h (b1 + b2 )

Consider a Trapezoid on the Coordinate Plane

Find the area of trapezoid MNPO:

Find b1 and b2: b1 = |-3 - 3| = 6 b2 = |-5 – 6| = 11Find h: h = |4 – (-1)| = 5

A = (1/2) h (b1 + b2) = (1/2) 5 (6 + 11) = (1/2) 5 (17) = (1/2) 85 u2

= 42.5 u2

How can we take what we have learned from our area formula for a triangle and

apply it to the formula for the area of a rhombus?

Let’s look at a Rhombus

Area of a Rhombus: = area of KFH + area of JFK + area of IFJ + area of HFI

= (1/2) ((1/2)d1)((1/2)d2) + (1/2)((1/2)d1)((1/2)d2) + (1/2)((1/2)d1)((1/2)d2) + (1/2)((1/2)d1)((1/2)d2)

= 4 [ (1/2) ((1/2)d1) ((1/2)d2) ]

=4 [ (1/2) ((1/2)d1) ((1/2)d2) ]

= (d1) ((1/2)d2)

A = (1/2) (d1) (d2)