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# Area and Perimeter using special right triangles

Solving Area and Perimeter with Special Right Trianlges, Pythagorean Theorem, and distance

by

Tweet## Terri Kokoszka

on 7 December 2012#### Transcript of Area and Perimeter using special right triangles

Finding Area of 2-D shapes using Special Right Triangles (30-60-90 & 45-45-90) Pythagorean Theorem, and Distance Formula What is Area? Area is the number of

1 x 1 square units it takes

to cover a 2 dimensional figure. Where is Area used in real life? Example 1:

Find the number of acres a farmer

owns. An acre is shaped like a

rectangle and measures

22 yards by 220 yards.

How many sq. yards

will the farmer owns? 4840 yd 2 Example 2:

A person wants to paint a room in

their house how much paint does

it take to cover the four walls?

Example 3:

Another person wants to lay tile

in their bathroom. How many

square feet of tile will they need

to purchase? Example 4:

A local business wants to wrap their

van with their company logo. How

many square feet of wrap will it

take to cover the whole van? Reviewing formulas Area Area Trapeziod Rhombus Parallelogram Rectangle

A=bh Square

A=s Triangle Rectangle

2l + 2w Square

and

Rhombus

4s All shapes

add all sides 2 bh 2 (b + b ) h 1 2 2 d d 1 2 2 bh Perimeter Sometimes it is necessary to find the missing

sides before you can find the area of a figure.

We are going to use some of the rules we’ve

learned so far this year to do this. 30-60-90 Triangle 60 30 x x 3 2x 30 60 18 45-45-90 Triangle 45 45 45 45 18 x x x 2 Pythagorean Theorem a b c 3 5 (a + b = c ) 2 2 2 (3 + b = 5 ) b = 5 - 3 b = 25 - 9 b = 16 b = 4 2 2 2 2 2 2 2 Distance Formula (3,5) (2,2) d= (x - x ) + (y - y ) 2 1 2 1 2 2 d= (3 - 2 ) + (5 - 2 ) d= (1) + (3) d= 1 + 9 d= 10 2 2 2 2 Find the Perimeter and Area for the triangle. Formula for Perimeter

P=add all sides First find the blank side using Pythagorean Theorem

also find the Height using Pythagorean Theorem x x= 52 P = 14 + 52 Find the approximate perimeter of a square with a diagonal length of 4 inches. 4 Answer- 11.31 in Find the approximate area of a square with a diagonal length of 4 inches. 4 Answer- 8 in Find the approximate perimeter

of the rectangle. 16 in 30 Answer- 43.71 in Find the approximate area

of the rectangle. 16 in 30 Answer is 110.85 in 2 2 You'll need to use a 30-60-90 triangle

to solve for the missing sides. You'll need to use a 45-45-90 triangle to solve for the missing sides. 45 6 in Find the approximate perimeter

of the triangle. You'll need to use a 45-45-90 triangle to solve for the missing sides. The answer is 14.49 in 45 6 in Find the approximate area

of the triangle. The answer is 9 in 2 Find the exact perimeter of the isosceles trapezoid in inches. 45 45 8 14 10 The Answer is 42 in 8 14 45 45 Find the approximate area of the isosceles trapezoid in inches. Use the 45-45-90 triangle to find

the height of the isosceles trapezoid. The answer is 33 in 2 14.2 cm 6.5 cm Find the approximate area

of triangle. The answer is 41.0 cm 2 Use Pythagorean Theorem

to solve for the missing side. 8 ft 12 ft Find Missing Measure.Trapezoid ABCD has an

area of 40 square feet. Find the height. The answer is 4 ft Find the Area and Perimeter of the parallelogram. 5 2 ft 45 A= 55 ft P= 22 + 10 2 Use 45-45-90 triangles to solve for the height. Area of a square on the Coordinate Plane

COORDINATE GEOMETRY Find the area of square WXYZ with vertices W (1, 6), X (5,2)Y (1, −2), and Z (−3, 2). Use the distance formula to find the length of each side. Then find the area. (1, 6) (-3, 2) (5, 2) (1, -2) S = 5.7, A = 32 Find the Area of the trapezoid. A= 53.04 m 2 Use Pythagorean Theorem. Find the Area of the Trapezoid. A= 49.8 ft 2 Find the Area of the kite in meters. A = 420 m There is several ways to solve for the area of the kite-

Use the area formula for a rhombus or find the area of the triangles. 2 The total area of trapezoid FGHJ is 52 square inches.

What is the approximate length of FJ? f J G H 2= 5 inches

4= 8 inches FJ = 8.5 inches 2 A = 18 ft Height = 4 ft 2 8 3 11 ft

Full transcript1 x 1 square units it takes

to cover a 2 dimensional figure. Where is Area used in real life? Example 1:

Find the number of acres a farmer

owns. An acre is shaped like a

rectangle and measures

22 yards by 220 yards.

How many sq. yards

will the farmer owns? 4840 yd 2 Example 2:

A person wants to paint a room in

their house how much paint does

it take to cover the four walls?

Example 3:

Another person wants to lay tile

in their bathroom. How many

square feet of tile will they need

to purchase? Example 4:

A local business wants to wrap their

van with their company logo. How

many square feet of wrap will it

take to cover the whole van? Reviewing formulas Area Area Trapeziod Rhombus Parallelogram Rectangle

A=bh Square

A=s Triangle Rectangle

2l + 2w Square

and

Rhombus

4s All shapes

add all sides 2 bh 2 (b + b ) h 1 2 2 d d 1 2 2 bh Perimeter Sometimes it is necessary to find the missing

sides before you can find the area of a figure.

We are going to use some of the rules we’ve

learned so far this year to do this. 30-60-90 Triangle 60 30 x x 3 2x 30 60 18 45-45-90 Triangle 45 45 45 45 18 x x x 2 Pythagorean Theorem a b c 3 5 (a + b = c ) 2 2 2 (3 + b = 5 ) b = 5 - 3 b = 25 - 9 b = 16 b = 4 2 2 2 2 2 2 2 Distance Formula (3,5) (2,2) d= (x - x ) + (y - y ) 2 1 2 1 2 2 d= (3 - 2 ) + (5 - 2 ) d= (1) + (3) d= 1 + 9 d= 10 2 2 2 2 Find the Perimeter and Area for the triangle. Formula for Perimeter

P=add all sides First find the blank side using Pythagorean Theorem

also find the Height using Pythagorean Theorem x x= 52 P = 14 + 52 Find the approximate perimeter of a square with a diagonal length of 4 inches. 4 Answer- 11.31 in Find the approximate area of a square with a diagonal length of 4 inches. 4 Answer- 8 in Find the approximate perimeter

of the rectangle. 16 in 30 Answer- 43.71 in Find the approximate area

of the rectangle. 16 in 30 Answer is 110.85 in 2 2 You'll need to use a 30-60-90 triangle

to solve for the missing sides. You'll need to use a 45-45-90 triangle to solve for the missing sides. 45 6 in Find the approximate perimeter

of the triangle. You'll need to use a 45-45-90 triangle to solve for the missing sides. The answer is 14.49 in 45 6 in Find the approximate area

of the triangle. The answer is 9 in 2 Find the exact perimeter of the isosceles trapezoid in inches. 45 45 8 14 10 The Answer is 42 in 8 14 45 45 Find the approximate area of the isosceles trapezoid in inches. Use the 45-45-90 triangle to find

the height of the isosceles trapezoid. The answer is 33 in 2 14.2 cm 6.5 cm Find the approximate area

of triangle. The answer is 41.0 cm 2 Use Pythagorean Theorem

to solve for the missing side. 8 ft 12 ft Find Missing Measure.Trapezoid ABCD has an

area of 40 square feet. Find the height. The answer is 4 ft Find the Area and Perimeter of the parallelogram. 5 2 ft 45 A= 55 ft P= 22 + 10 2 Use 45-45-90 triangles to solve for the height. Area of a square on the Coordinate Plane

COORDINATE GEOMETRY Find the area of square WXYZ with vertices W (1, 6), X (5,2)Y (1, −2), and Z (−3, 2). Use the distance formula to find the length of each side. Then find the area. (1, 6) (-3, 2) (5, 2) (1, -2) S = 5.7, A = 32 Find the Area of the trapezoid. A= 53.04 m 2 Use Pythagorean Theorem. Find the Area of the Trapezoid. A= 49.8 ft 2 Find the Area of the kite in meters. A = 420 m There is several ways to solve for the area of the kite-

Use the area formula for a rhombus or find the area of the triangles. 2 The total area of trapezoid FGHJ is 52 square inches.

What is the approximate length of FJ? f J G H 2= 5 inches

4= 8 inches FJ = 8.5 inches 2 A = 18 ft Height = 4 ft 2 8 3 11 ft