Spring Board Unit 5 - Geometry

Monday April 1, 2013 Warm Up Get your spiral out of the cabinet. Find and write down the formulas used to find the area of a Rectangle, and a Triangle. Label what each letter in the formula means.

What is Two-Dimensional Geometry? Polygons are shapes (or closed figures) made up of three or more line segments. Some types of polygons are: Square Rectangle Parallelogram Triangle Trapezoid

What is Two-Dimensional Geometry? Polygons have two dimensions which are: Base – which is the distance across the bottom of the shape. Height – which is always perpendicular to the base. There is a red dashed square which shows the right angle where the height meets the base. For Example: base – 10 meters Height – 5 meters Right angles are perfect corners!

What is Two-Dimensional Geometry? Two dimensional shapes are flat. Sometimes they are referred to as “plane” figures. This means you could: Hang them on the wall Put them on the desk Lay them on the floor Pin them to a bulletin board.

What Do You Need to Know About Shapes? What is the distance around the shape? How much space is inside the shape?

What Do You Need to Know About Shapes? The distance around the shape is called the perimeter. The space is inside the shape is called the area.

How Do You Find the Perimeter? In many cases you can find the perimeter of a shape by simply adding up all of the sides. Since there are two sides and a bottom and a top you can write: perimeter = 4 + 4 + 2 + 2 Or p = 10 feet 4 feet 2 feet

How Do You Find the Perimeter? Sometimes a measurement is missing. Since the top is the same length as the bottom, you know that the top is also 4 feet. Since the left side is 2 feet, you know that the right side is also 2 feet. 4 feet 2 feet

How Do You Find the Perimeter? Always find all missing measurements before finding the perimeter. The long side on the right is equal to the lengths of both of the shorter sides on the left: 2.3 + 4.1 = 6.4 cm The short side on the bottom is equal to the length of the top minus the longer side on the bottom: 5.2 – 3.9 = 1.3 cm

How Do You Find the Perimeter? To find the perimeter add up all of the sides. 2.3 5.2 6.4 1.3 4.1 + 3.9 23.2 cm 6.4 cm 1.3 cm

How Do You Find the Area? Sometimes you can find the area of a shape by counting the blocks inside the figure. Since there are eight smaller blocks within the rectangle, the area is 8 square feet. 4 feet 2 feet 1 2 3 4 5 6 7 8

How Do You Find the Area? You may have noticed that you can find the area by multiplying the base (or 4) by the height (or 2). A = bh A = 4 × 2 A = 8 square feet 4 feet 2 feet 1 2 3 4 5 6 7 8

Using the FCAT Reference Sheet The Grades 6-8 FCAT 2.0 Mathematics Reference Sheet is given to every student during the Mathematics FCAT test. It contains ALL of the formulas for the areas of two dimensional shapes. It also contains other important math facts!

Using the FCAT Reference Sheet Here are the area formulas:

Using the FCAT Reference Sheet Here is the key for use with the formulas:

Complete the problem on your paper April 8, 2013 Warm-Up Materials Binder or Folder Paper for Notes Complete the problem on your paper

Find Area of a Rectangle Select the correct area formula:

Find Area of a Rectangle Write the area formula exactly as it appears on the FCAT Reference Sheet. Rewrite the area formula substituting the values that you know. Solve one step at a time rewriting after each step. A = bh A = 7.3 × 4.2 A = 30.66 square feet

Find Area of a Parallelogram Determine which measurement is the height: The height is inside the parallelogram The height is outside the parallelogram The height is inside or outside the parallelogram but another side measurement is given to confuse you.

Find Area of a Parallelogram Select the correct area formula:

Find Area of a Parallelogram Write the area formula exactly as it appears on the FCAT Reference Sheet. Rewrite the area formula substituting the values that you know. Solve one step at a time rewriting after each step. A = bh A = 8 × 9 A = 72 square centimeters

Why is Area in Square Units? Remember that the shapes have two dimensions. When you multiply one measurement by another measurement you end up with square units. For Example: Square Feet ft2 Square Inches in2 Square Centimeters cm2

Find the Area of the Following Shapes The large rectangle in the center. The parallelogram beneath the rectangle.

Find the Area of the Following Shapes A = bh A = 10 × 6 A = 60 sq. meters A = bh A = 3 × 7 A = 21 sq. meters

How Do You Solve for a Missing Measurement? Follow the same set of steps as before! Write the area formula exactly as it appears on the FCAT Reference Sheet. Rewrite the area formula substituting the values that you know. Solve one step at a time rewriting after each step.

How Do You Solve for a Missing Measurement? Solve the following problem: Find the height of a parallelogram if its base is 9 feet and its area is 27 square feet. A = bh = 9 × h Divide by 9 on both sides to undo the multiplication! 3 ft = h

How Do You Solve for a Missing Measurement? Solve the following problem: Find the base of a parallelogram with an area of 18 square inches and a height of 2 inches. A = bh 18 = b × 2 Divide by 2 on both sides to undo the multiplication! 9 in = b

Time to Practice Remember to use the area formulas on the FCAT Reference Sheet: