Unit 5: Measurement (in 2D and 3D) Learning Target: I can explain the different growth rates of 1 dimensional and 2 dimensional measurements Unit 5: Measurement (in 2D and 3D) Do Now 4/13: What is the area of the rectangle below? What would be the area of a rectangle if every side was 2 times longer? Agenda: 1. Do Now 2. Penny Problem 3. Penny Presentations 4. Debrief 3 in 7 in

1D vs. 2D Models/ Area Formulas Learning Target: I can use models to explain the different growth rates of 1 dimensional and 2 dimensional measurements 1D vs. 2D Models/ Area Formulas Do Now 4/14: Find the area of the triangle below. Agenda: 1. Do Now 2. Complete Penny Problem 3. Present and Debrief 4. Review: Area formulas 13 cm 12 cm

How many pennies can fit in a circle with a diameter of 22in? Estimates Too High Too Low Strategies/Methods Known Information Answer: Equation:

Deriving Area Formulas Learning Target: I can use the area formula of a triangle to derive the formula for a regular polygon. Deriving Area Formulas Do Now 4/14: Find the area of the trapezoid below. 6cm 2 cm 8 cm Agenda: 1. Do Now 2. Penny Problem Answers 3. HW Review 3. Area of a Regular Polygon 4. Debrief/Exit Ticket 8 cm 2 cm

Review: Area of Triangle The area formula for a triangle is A = ½ bh H or height, is also known as the altitude, is ALWAYS perpendicular to the base. h b

Review: Area of Trapezoid The area formula for a trapezoid is A = ½ (b1+b2)h H or height, is also known as the altitude, is ALWAYS perpendicular to the base. b1 h b2

Create a Regular Polygon Regular – all equal sides and all equal angles Draw a circle using a compass Divide that circle into equal sections. (Hint: Try using degrees) Connect each point with a straight line. How many sides does your polygon have? What is it’s name?

Apothem The apothem is the perpendicular distance from the center of an inscribed polygon to the midpoint of the side. How is the apothem related to area of a triangle?

Interior Angle of a Regular Polygon How many degrees are each central angle? How many degrees are each inscribed angle? How can we generalize this to write a rule/formula that find the interior angle of ANY polygon?

Debrief/Exit Ticket Interior Angle = 180 - (360/n) How can we use the area formula of a triangle to find the area of our regular polygon? Using the area formula for a triangle, generalize your answer to the question above to write a rule/formula for a regular polygon. Interior Angle = 180 - (360/n) Areareg = ½(s)(a)(n) s = length of side a = length of apothem n = number of sides

Using Trig with Regular Polygons Learning Target: I can use trigonometry to find the apothem of a regular polygon. Using Trig with Regular Polygons Do Now 4/13: What is the area of the regular polygon below? Agenda: 1. Do Now 2. HW Review 3. Regular Polygons and Trig 4. Debrief 3 in 7 in

Regular Polygons, if Missing Apothem If the apothem is not given, then we may need to use Pythagorean Theorem or Trigonometry to find it. First, the apothem will bisect the side, and form two right triangles. If we know the radius, we can then use Pythagorean Theorem. If we don’t know any other information, we can find the angles in the triangle using the Interior Angle of a Regular Polygon, and use Trigonometry to find the apothem. ? 10 in 10 in

Guided Practice Find the area of each figure. 2 3.5

Debrief When will we need to use Pythagorean Theorem to find the apothem? When will we need to use trigonometry?