Let’s Talk Triangles & Parallelograms

These are parallelograms!

Area of a Parallelogram quadrilateral A parallelogram is a _______________ whose opposite sides are _________. Area of a parallelogram = parallel base x height Since a rectangle is a type of parallelogram, the area formula is exactly the same!!

Let’s talk about height for a moment… Select two students and measure their heights

What is the height of each parallelogram? 4 cm 5 cm 4 ft 8 ft 13 cm 5 ft 2 in 12 in 9 in

Area of a parallelogram: A = bh Which measurements will we use? Fill in the formula Write your answer and label your units. h = 4 ft 5 ft 4 ft b = 8 ft 8 ft 5 ft is not the height!! We won’t use this in our area calculation! A = (4)(8) = 32 A = 32ft2

Area of a parallelogram: A = bh Which measurements will we use? Fill in the formula Write your answer and label your units. h = 8 ft 12 ft 8 ft b = 20 ft 20 ft A = (8)(20) = 160 A = 160 ft2

Area of a parallelogram: A = bh Which measurements will we use? Fill in the formula Write your answer and label your units. h = 6 in 7 in 6 in b = 5 in 5 in A = (6)(5) = 30 A = 30 in2

1) 2) 3) Calculate the area: 5 ft 7 ft 8 ft 1.5 in 5 in 2.5 in 10.05 cm 3) 3.4 cm 6.5 cm

Let’s examine something… A triangle can be thought of as half of a parallelogram.

What would be the formula for the area of a triangle? Riddle me this… We just calculated how to find the area of a parallelogram. A = bh If a triangle is simply half of a parallelogram, then… What would be the formula for the area of a triangle?

If we have a parallelogram… A = bh 8(3) = 24 ft2 3 ft 4 ft 8 ft What is the area of just this triangle? = 12 ft2

Area of a triangle AREA OF A TRIANGLE Words Numbers Formula Triangle: The area A of a triangle is one-half the base length b times the height h. A = (8)(4) = 16 units2 1 2

A = Area of a triangle: A = 16 ft2 h = 4 ft b = 8 ft (4)(8) = (32) Which measurements will we use? Fill in the formula Write your answer and label your units. h = 4 ft 4 ft b = 8 ft 8 ft 1 1 A = (4)(8) = (32) = 16 2 2 A = 16 ft2

A = Area of a triangle: A = 75 in2 h = 10 in b = 15 in (10)(15) = Which measurements will we use? Fill in the formula Write your answer and label your units. h = 10 in 10 in b = 15 in 15 in 1 1 A = (10)(15) = (150) = 75 2 2 A = 75 in2

A = Area of a triangle: A = 30 cm2 h = 5 cm b = 12 cm (5)(12) = (60) Which measurements will we use? Fill in the formula Write your answer and label your units. 14 cm h = 5 cm 6 cm 5 cm b = 12 cm 12 cm 1 1 A = (5)(12) = (60) = 30 2 2 A = 30 cm2

A = Area of a triangle: A = 33 ft2 h = 6 ft b = 11 ft (6)(11) = (66) Which measurements will we use? Fill in the formula Write your answer and label your units. 14 ft h = 6 ft 6 ft b = 11 ft 11 ft 1 1 A = (6)(11) = (66) = 33 2 2 A = 33 ft2

1) 2) 3) Calculate the area: 5 in 3 in 12 in 4.5 ft 2.3 ft 8.7 cm

Keypoint! The base of a triangle is not always the bottom side!!!

Let’s try one! Graph and find the area of the figure with the given vertices. (–2, 2), (4, 2), (0, 5) Area of a triangle A = bh 1 2 (0, 5) Substitute for b and h. = • 6 • 3 1 2 (–2, 2) (4, 2) 6 = 9 units2