DescriptionStudents use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons. Students learn through exploration that the area of a triangle is exactly half of the area of its corresponding rectangle. They extend their previous knowledge about the area formula for rectangles to evaluate the area of the rectangle using A = bh and discover through manipulation that the area of a right triangle is exactly half that of its corresponding rectangle. Show Students discover that triangles have altitude, which is the length of the height of the triangle. The altitude is the perpendicular segment from a vertex of a triangle to the line containing the opposite side. The opposite side is called the base. Students understand that any side of the triangle can be a base, but the altitude always determines the base. They move from recognizing right triangles as categories to determining that right triangles are constructed when altitudes are perpendicular and meet the base at one side. Acute triangles are constructed when the altitude is perpendicular and meets within the length of the base, and obtuse triangles are constructed when the altitude is perpendicular and lies outside the length of the base. Students use this information to cut triangular pieces and rearrange them to fit exactly within one half of the corresponding rectangle to determine that the area formula for any triangle can be determined using A = 1/2(bh). CreditsFrom EngageNY.org of the New York State Education Department. Grade 6 Mathematics Module 5, Topic A, Overview. Available from engageny.org/resource/grade-6-mathematics-module-5-topic-overview; accessed 2015-05-29. Copyright © 2015 Great Minds. UnboundEd is not affiliated with the copyright holder of this work.
 Since the area of a parallelogram is A = B * H, the area of a triangle must be one-half the area of a parallelogram. Thus, the formula for the area of a triangle is: where b is the base, h is the height and · means multiply. The base and height of a triangle must be perpendicular to each other. In each of the examples below, the base is a side of the triangle. However, depending on the triangle, the height may or may not be a side of the triangle. For example, in the right triangle in Example 2, the height is a side of the triangle since it is perpendicular to the base. In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height. Example 1: Find the area of an acute triangle with a base of 15 inches and a height of 4 inches. Solution: Example 2: Find the area of a right triangle with a base of 6 centimeters and a height of 9 centimeters. Example 3: Find the area of an obtuse triangle with a base of 5 inches and a height of 8 inches. Solution: Example 4: A triangle shaped mat has an area of 18 square feet and the base is 3 feet. Find the height. (Note: The triangle in the illustration to the right is NOT drawn to scale.) Solution: In this example, we are given the area of a triangle and one dimension, and we are asked to work backwards to find the other dimension. 18 ft2 = Multiplying both sides of the equation by 2, we get: 36 ft2 = (3 ft) · h Dividing both sides of the equation by 3 ft, we get: 12 ft = h Commuting this equation, we get: h = 12 ft Summary: Given the base and the height of a triangle, we can find the area. Given the area and either the base or the height of a triangle, we can find the other dimension. The formula for area of a triangle is: ExercisesDirections: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. Your answers should be given as whole numbers greater than zero. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Sign Up For Our FREE Newsletter!Sign Up For Our FREE Newsletter!What is the meaning of triangle in math?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC. Examples of Triangles.
What is the formula of area of polygon?The formula for calculating the area of a regular polygon is A = (n/2) * L * R, where n is the number of sides in the polygon, L is the length of one side of the polygon, and R is the radius of an inscribed circle.
What is the area of this given triangle?The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
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Lesson 2 find the area of triangles and other polygons
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