WINNIE LIANG JESSICA SZELA EMMA GRACE MEDALLA JENICE XIAO ALGEBRA 2/TRIGONOMETRY PERIOD 8.

Slides:



Advertisements
Similar presentations
Circle – Formulas Radius of the circle is generally denoted by letter R. Diameter of the circle D = 2 × R Circumference of the circle C = 2 ×  × R (
Advertisements

9.6 Apply the Law of Cosines In which cases can the law of cosines be used to solve a triangle? What is Heron’s Area Formula? What is the semiperimeter?
By Trissy Brandvold. What type of triangle is this? equilateral triangle right triangle isosceles triangle.
10.2The Law of Sines Objectives: 1. Solve oblique triangles by using the Law of Sines. 2. Use area formulas to find areas of triangles.
Today, I will learn the formula for finding the area of a rectangle.
Aim: How can we find the area of a Triangle using Heron’s Formula
Green text p.138 #s The length of the second side of a triangle is 2 inches less than the length of the first side. The length of the third.
6-2 Warm Up Problem of the Day Lesson Presentation
4.6 – AREA FORMULAS. Formulas from yesterday: Perim.of a Rect.= Area of a Rect.=
Hero’s and Brahmagupta’s Formulas Lesson Hero of Alexandria He was an ancient Greek mathematician and engineer who was born in 10 AD. He invented.
Area of Regular Polygons 5.5
11.8 Hero’s and Brahmagupta’s Formulas. T111:A ∆ = a b c Where a, b, c are length’s of the sides and s = semi-perimeter S = a + b + c 2 Area of a triangle:
Geometry Section 9.4 Special Right Triangle Formulas
6-2 Warm Up Problem of the Day Lesson Presentation
11.8 Hero’s and Brahmagupta’s Formulas Objective: After studying this section you will be able to find the areas of figures by using Hero’s and Brahmagupta’s.
What is Trigonometry? Trigonometry (from the Greek trigonon = three angles and metron = measure) is a part of elementary mathematics dealing with angles,
Special Right Triangles Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =
AREA OF A TRIANGLE. Given two sides and an included angle:
Perimeter with Variables code-it.co.uk. The weather is variable His moods are variable.
10.3 Areas of Regular Polygons
Chapter 10 Test Formula Review.  Find the circumference of a circle with a diameter of 10. Identify the formula needed for the following questions.
Heron’s Formula. Heron’s Formula is used to determine the area of any triangle when only the lengths of the three sides are known.
Pg. 435 Homework Pg. 443#1 – 10 all, 13 – 18 all #3ɣ = 110°, a = 12.86, c = 18.79#4No triangle possible #5α = 90°, ɣ = 60°, c = #6b = 4.61, c = 4.84,
Working with Variables code-it.co.uk. Variable means changeable The weather is variable His moods are variable.
Basic Measurement.
6-2 Warm Up Problem of the Day Lesson Presentation
Bellwork Add the special formula for the equilateral triangle below to your toolbox. Find the area of an equilateral triangle with a side of.
EXAMPLE 1 Finding Area and Perimeter of a Triangle Find the area and perimeter of the triangle. A = bh 1 2 P = a + b + c = (14) (12) 1 2 =
EXAMPLE 3 Standardized Test Practice A = lw 63 = 9w 63 = = w Write area formula. Substitute values. Divide each side by 9. Simplify. ANSWERThe.
Write an algebraic expression to represent 5 less than a number “n”.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
Area & Perimeter of Triangles. The formula for a triangle can be determined from using parallelograms. Cut a parallelogram in half it forms 2 triangles.
3-8 Solving Equations and Formulas Objective Students will be able to solve equations for given variables.
Area of regular polygons
Area and Perimeter Quiz
The length of a rectangle is twice the width. The perimeter is 72 inches. Find the length and the width of the rectangle.
Inscribed and Circumscribed Circles Dr. Jason Gershman.
SUBMITTED TO GAGAN MAM MATHS HOLIDAYS HOMEWORK. TOPIC : HERON’S FORMULA.
Investigating the Area of Polygons Area of triangles Angles inside polygons Geometric reasoning Surds Simplifying algebra Pythagoras Trigonometry.
30 ° 60 ° s S2S2 S√3 2 A= s 2 √3 4 A= s 2 √3 4 S= 3 A= 3 2 √3 4 A= 9√3 4 A≈ 3.9.
Good Morning, Precalculus! To prepare for class: 1. Please find your DO NOW sheet and start today's DO NOW! 2. Take out your homework: worksheet 5-6 Do.
AREAS OF TRIANGLES Methods for Finding the Area of Oblique Triangles.
6.2 Laws of Cosines. Law of Cosines Find all the parts of a triangle.
Heron's formula In geometry, Heron's (or Hero's) formula, named after Heron of Alexandria, [1] states that the area T of a triangle whose sides have lengths.
S ECTION 5-6 Law of Cosines & Area. S ECTION 5-6 the Law of Cosines solving triangles (SSS and SAS) finding the area of a triangle (SAS) Heron’s Formula.
Section 8.4 Area of a Triangle. Note: s is the “semi-perimeter.”
Algebra 2. Do this First! For Review Algebra 2.
Law of Sines Use it when you are given Angle-Angle-Side (AAS) Angle-Side-Angle (ASA) Side-Side-Angle (SSA)
Area of Triangles Section 5.6 The Area of a Triangle Using Trigonometry Therefore, we can find the area of a triangle if we are given any two sides of.
GEOMETRY REVIEW.
EXAMPLE 1 Finding Area and Perimeter of a Triangle
Area and Perimeter 6th grade math.
Section 7.2 Perimeter and Area of Polygons
Theorem The area A of a triangle is
a2 + b2 = c2 Pythagorean Theorem c c b b a a
Section 8.2 Perimeter and Area of Polygons
Solving Problems Involving Geometry
Lesson 11.2 Prisms pp
Lesson 8.3 Pythagorean Theorem pp
Algebra 1 Section 11.3.
17 Area of a Triangle.
Perimeter.
Standards:.
If a triangle is a RIGHT TRIANGLE, then a2 + b2 = c2.
By- Sabrina,Julianna, and Killian
T3.1b To Find The Area Of Any Triangle Given Three Sides
Day 116 – Perimeter and area of a triangle on x-y plane
Laws of Sines and Cosines
Heron’s Formula Winnie Liang Jessica Szela Emma Grace Medalla
Area and Perimeter Triangles.
Presentation transcript:

WINNIE LIANG JESSICA SZELA EMMA GRACE MEDALLA JENICE XIAO ALGEBRA 2/TRIGONOMETRY PERIOD 8

AIM: WHAT IS HERON’S FORMULA AND HOW DO WE USE IT? Do Now: Find the area. 6 in 8 in 1) Area of triangle = b  h 2 A = 8  6 2 A = 48 2 A = 24 in 2 3 in6 in 8 in 2)

THE HERON’S FORMULA IS USED TO FIND THE AREA OF A TRIANGLE USING ITS SIDES. The formula is credited to Heron, who was the “Hero of Alexandria”; a proof can be found in his book, Metrica written in 60 A.D. It was discovered by the Chinese published in Shushu Jiuzhang.

“S” is half the triangle’s perimeter A, B, and C are the sides of the triangle.

THE HERON’S FORMULA: After using the formula to find “s,” you plug it into the Heron’s formula and again a, b, and c refer to the sides of the triangle.

EXAMPLES: 1)What is the area of the triangle with sides of length 10 feet, 15 feet, and 17 feet?

2) What is the area of an equilateral triangle with all sides 6 inches in length?

NOW TRY THE DO NOW QUESTION 2) semiperimeter = a + b + c 2 s = s = 17 2 s = 8.5 A = √ s(s – a)(s – b)(s – c) A = √ 8.5(8.5 – 3)(8.5 – 6)(8.5 – 8) A = √ 8.5(5.5)(2.5)(0.5) A ≈ 7.64 in 2 3 in6 in 8 in 2)