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Area and Perimeter using special right triangles

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

Terri Kokoszka

on 7 December 2012

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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
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