Area of Quadrilaterals and Triangles

Geom Section 7.1 Area of Quads and Triangles.

​

Fill in the Blank

What is the area of this shape?

Multiple Choice

Give the most specific name of the quadrilateral?

• Rectangle

• Square

• Parallelogram

• Kite

• Rhombus

Multiple Choice

Give the most specific name of the quadrilateral?

• Rectangle

• Square

• Parallelogram

• Kite

• Rhombus

Multiple Choice

Give the most specific name of the quadrilateral?

• Rectangle

• Square

• Parallelogram

• Kite

• Rhombus

Multiple Choice

Give the most specific name of the quadrilateral?

• Rectangle

• Square

• Parallelogram

• Kite

• Rhombus

Multiple Select

Which of these quadrilaterals are parallelograms?

• Rectangle

• Square

• Trapezoid

• Kite

• Rhombus

A = b h

Parallelograms

• A parallelogram is a 4 sided figure whose opposite sides are parallel lines.

• Any line can be called the base.

• The height is perpendicular to the base and connects to the opposite side.

A segment drawn from a vertex that is perpendicular to the line containing the opposite side of the polygon. This is known as the height.
The side to which it is perpendicular is the base.

​

Altitude

​We can rearrange the parallelogram so that it makes a rectangle!

​

This means that we can use the same FORMULA!!​ 😀

​​Let's Watch a small demo

We have the following parallelogram.

​

As we can see we have a bottom length or base of 6 units. The height is 3 units tall.​

Example application of using the formula

Example 1

1. Identify what we know:

   b = 6 units h = 3 units

2. Plug into Equation

   A = 6 x 3

3. Solve

   A = 18 units²

Fill in the Blank

What is the area of the parallelogram?

Multiple Select

What can be said about the triangles created by the diagonal drawn in the parallelogram?

(More than one is true

• Triangles ABD and CDB are congruent by SSS

• Triangles ABD and CDB are congruent by SAS

• Triangles ABD and CDB are similar by SAS

• Triangles ABD and CDB are similar by SSS

Multiple Choice

What is the area of the triangle?

• 48

• 24

• 60

• 30

• 42

Multiple Choice

Find the area of the triangle.

• 110

• 55

• 45

• 10

Multiple Choice

Find the area of the special triangle.

(What makes this so special?)

• 48

• 40

• 30

• 24

Multiple Choice

Find the area of the special triangle.

A great question with a final exam right around the corner . . .

• $$36\sqrt{3}$$

• $$18\sqrt{3}$$
  

• 36

• 72

Multiple Choice

True or false.

Two figures that have the same area must be congruent.

• True

• False

Multiple Choice

True or false.

Two figures with the same area must have the same perimeter.

• True

• False

Multiple Choice

True or false.

Two figures that are congruent must have the same area.

• True

• False

Homework

• Formative 7.1