Area of Shapes

Area of Shapes

What is Area?

• Area is the size of the flat surface

• It is measure in units squared, or units²

Rectangles

Area of a Rectangle

• Use the formula: A=bh

• b = length of the base

• h = height of the rectangle

Example 1: Find the area

•  $A\ =\ bh$  

• b = 8.6

• h = 3

•  $A\ =\ 8.6\left(3\right)$  

•  $A\ =\ 25.8\ cm^2$  

Example 2: Find Area

• A = bh

•  $b\ =\ 2\ \frac{1}{4}$  

•  $h\ =\ 1\ \frac{1}{2}$  

•  $A\ =\ 2\ \frac{1}{4}\ \left(1\ \frac{1}{2}\right)$  

•  $A\ =\ 3\ \frac{3}{8}\ ft^2$  

Fill in the Blank

Two walls of a room are being painted. Each wall measures 16 ft by 8 1/2 ft.

How many square feet will be painted?

Writing Formulas

• Formulas can be manipulated to solve for missing information.

• EX: A = bh can be manipulated

• Divide the h to the other side:  $b\ =\ \frac{A}{h}$ 

• Divide the b to the other side:  $h\ =\ \frac{A}{b}$ 

Example 3: The area of the rectangle is 162 m²

• We know A and H, but not B.

• Use:  $b\ =\ \frac{A}{h}$  

•  $b\ =\ \frac{162}{18}$  

•  $b=9m$  

Multiple Select

Check all of the formulas below that could be used to find the height of a rectangle with a base of 11 in and an area of 120 in²

• $120\ =\ 11\left(11\right)$

• $120\ =\ 11\left(h\right)$

• $11\ =\ 120\left(h\right)$

• $h\ =\ \frac{120}{11}$

• $h\ =\ \frac{11}{120}$

Fill in the Blank

A rectangular canvas covers 225 in² on a wall. If the canvas has a height of 18 in, then what is the base?

A = b*h

Area of Parallelograms

• The dimensions of a parallelogram are also referred to as the base and height.

• Use the formula A=bh.

• B is the length of the base.

• H is the height of the parallelogram, which makes a 90-degree angle with the base.

• H is the perpendicular height.

Example 4: Find area

•  $A=bh$  

• b = 12.2cm

• h = 8cm, as it is perpendicular to the base.

•  $A\ =\ 12.2\left(8\right)$  

•  $A=97.6cm^2$  

Fill in the Blank

Find the area of the following rectangle.

Open Ended

Describe how the area of a rectangle and the area of a parallelogram with the same dimensions are related.

Think on the formulas.

Triangles

Area of Triangles

• Two triangles are formed when a parallelogram is cut in half

• Therefore, the formula for the area of a triangle is:  $A\ =\ \frac{bh}{2}$  

• The height of the triangle will form a right angle with the base. It is the perpendicular height.

Multiple Select

Check all statements that are correct.

• b=14

• h=14

• b=16

• h=16

• A=112 in²

Fill in the Blank

Find the area.

 $A\ =\ \frac{bh}{2}$  

Fill in the Blank

What is the area of a right triangle with a height of 8.9cm and a base of 14.3 cm?

Trapezoids

Area of Trapezoids

• A trapezoid is one or two triangles and a rectangle combined.

• Use the formula:  $A=\frac{b_1\ +\ b_2}{2}\ \cdot\ h$  

• b1 is the length of the 1st base

• b2 is the length of the 2nd base

• h is the perpendicular height of the trapezoid.

Example 5: Find area

• Formula:  $A\ =\ \frac{b_1+b_2}{2}\ \cdot\ h$  

• b1=12 ; b2=7 ; h=4

•  $A=\frac{12+7}{2}\cdot4$  

•  $A=\frac{19}{2}\cdot4$  

•  $A=\frac{76}{2}$  

•  $A=38in^2$  

Multiple Choice

Find the area of the regular trapezoid.

• 108 in2

• 60 in2

• 27 in2

• 54 in2

Fill in the Blank

Find the area of the trapezoid by breaking it into a rectangle and a triangle.
All information needed is provided.
Area Rectangle: A=bh ; Area of Triangle:  $A\ =\ \frac{bh}{2}$