Understanding the Pythagorean Theorem through Triangle Area Calculation

Jun 16, 2025

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Learn how to find the area of a triangle using the Pythagorean Theorem and explore the history behind this fundamental concept. Discover the relationship between the sides of a right triangle with A^2 + B^2 = C^2.

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Understanding the Pythagorean Theorem through Triangle Area Calculation

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HOW TO FIND THE AREA OF A TRIANGLE By: Dallas Rekow
PYTHAGOREAN THEORAM A2+B2=C2
History the Pythagorean theorem

Area of a triangle

Area of a triangle. height. height. base. base. The area of a triangle is equal to half the area of the rectangle that can be drawn with the same base and height. The Area of the triangle can thus be calculated using the formula Area = ½ base x height or in algebraic form A= ½ bh.

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The Area of a Triangle

The Area of a Triangle. presents. Nipissing University Mathematics Lecture Talks. It Is More Complicated Than You Might Think!. Area is a physical quantity expressing the size of a part of a surface. . Surface area is the summation of the areas of the exposed sides of an object. .

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Using Trigonometry to find area of a triangle

Using Trigonometry to find area of a triangle. The area of a triangle is one half the product of the lengths of two sides and sine of the included angle. Area of ABC = ½ bc (sin A). B. a. c. C. A. b. Area of a Triangle. In . ABC is a non-right angled triangle. .

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Area of a Triangle

Area of a Triangle . What is a triangle?. All t riangles are related to rectangles or parallelograms :. You can draw a diagonal line in any rectangle or parallelogram. Each rectangle or parallelogram is made up of two triangles!. What is the Area of a Triangle?.

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Area of a Triangle

Area of a Triangle. 1 gram = __ milligrams. 1000. Area of a Triangle. 1 pound = __ ounces. 16. Volume of a Rectangular Prism. lwh. 1 meter = __ centimeters. 100. Area of a Trapezoid. lw. Area of a rectangle. a 2 + b 2 = c 2. Pythagorean Theorem. Area of a Trapezoid.

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Aim: How can we find the area of a Triangle using Heron’s Formula

Aim: How can we find the area of a Triangle using Heron’s Formula. Do Now:. A. Find the area of triangle ADC. Round to the nearest tenth. 12. X. Answer: Area=35.8. C. 8. B. Facts About Heron’s Formula.

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How to find the area of a parallelogram.

How to find the area of a parallelogram. The area of a parallelogram is base x height. 5 cm. 8cm. Area = 8 x 5 = 40cm 2. Here’s why:. A parallelogram can be split up into a rectangle and 2 triangles – each with the same area. 5 cm. 10cm. Here’s why:.

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Area of a triangle

Area of a triangle.

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How to find the area of a circle

How to find the area of a circle. By Sierra Lewis. Things to know. R. What is this ??. What is this ??. forbes.com. “r “ means radius which is half of the diameter or half way through the circle. That is pie not like the food “pie’ the number which is 22/7 in fraction form.

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How to Find the Area of a Circle

How to Find the Area of a Circle. Tori LeAnn Watson 5 th period. Parts of The Circle You Need to Know. This is the diameter. This is the radius. This is the circumference. ( The distance around the circle). Formula. The formula for finding the area of a circle is. For pi we use 3.14.

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How do you find the area of a right triangle?

How do you find the area of a right triangle?. In this lesson you will learn how to find the area of a right triangle by composing a rectangle. You find the area of a rectangle by multiplying length times width. width. length. Only finding the area of a rectangle and not the triangle.

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How to Find the Area of a Circle

How to Find the Area of a Circle. by : Rachel Sorenson. First lets take a look at the parts of a circle. This is the Radius. * The radius is a line segment reaching one point on the perimeter to the center of the c ircle. This is the diamete r.

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Area of a Triangle

Area of a Triangle. Activity: Draw a rectangle measuring 6cm by 3cm using a ruler in your notebook Draw a triangle inside the rectangle so that: a) at least one side of the triangle matches up with one side of the rectangle

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Area of a Triangle

Area of a Triangle. A= ½bh or A=bh÷2 Area equals one half times base times height OR Area equals base times height divided by two. Area of a Parallelogram. A= bh Area equals base times height. Area of a square/rectangle. A= bh OR A= lw Area equals base times height OR

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AREA OF A TRIANGLE

AREA OF A TRIANGLE. E. F. D. A. O. h units. B. C. a units. Consider a triangle ABC having BC = a units. Draw the height AD= h units. Draw a line EF, dividing the height AD in equal parts at O. A. E. O. F. B. C. Cut the upper triangles AEO & AOF. E. F. D. A. E. O.

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Objectives: find area of a parallelogram and triangle

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Area of a Triangle 7.3

Area of a Triangle 7.3. JMerrill, 2009. Area of a Triangle (Formula) . When the lengths of 2 sides of a triangle and the measure of the included angle are known, the triangle is uniquely determined. Use: S = ½ ab sin C S = ½ bc sin A S = ½ ac sin B.

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Area of a Triangle

Area of a Triangle. Right Triangle: Area = ½ base * height A triangle with a given angle: Area = ½ a*b* sinC Area of a triangle with no given angles Use Heron’s Formula Area = √(s(s-a)(s-b)(s-c)), where s = (a + b + c)/2. Law of Cosines Applications – cont’d.

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How to find the equation of an altitude of a triangle.

How to find the equation of an altitude of a triangle. Find the equation of the altitude BL. Find the equation of the altitude BL. 1. Sketch altitude from B to opposite side. L. Find the equation of the altitude BL. 1. Sketch altitude from B to opposite side.

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How to find the Area of the triangle

How to find the Area of the triangle. By Isabel Gonzalez. First lets take a look at the right triangle. A right triangle has one angle that is 90 degrees. 90 degree angle. Each side of the triangle has its own name. H ypotenuse. Leg A. We call this one c. Leg B.

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Area of a Triangle

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad , Glen Whiffen , John Owen, Robert Haese , Sandra Haese and Mark Bruce Haese and Haese Publications, 2004. Chapter 10 – Section F: Area of Triangles. Area of a Triangle.

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Aim: How do we find the area of triangle using trigonometry?

Aim: How do we find the area of triangle using trigonometry?. Do Now: In the diagram, ∆ ABC and h is the height. 1. Find the area of ∆ ABC. A. 2. Find sin C. b. c. h. C. B. a. HW: p.563 # 4,6,10,12,19,20. Area of triangle.

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