Understanding Area and Angles of Circles, Triangles, and Trapezoids

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This document provides a comprehensive overview of various geometric concepts, including the total degrees in a circle, calculations related to the area of triangles, circles, and trapezoids, along with their respective formulas. It delves into the relationships between angles and areas in polygonal shapes, illustrating how to compute the area using specific formulas such as A = 1/2 * (b1 + b2) * h for trapezoids and A = π * r² for circles. Helpful for students and professionals looking to understand the fundamental principles of geometry.

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Apr 28, 2026

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Understanding Area and Angles of Circles, Triangles, and Trapezoids

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total desired circles polygons
3 2 1 1 1 = 8 6 4 2 3

A circle has 360o total degrees. 180 - 45 Half a circle has 180o degrees. 135o 120o 180 - 60 135 3 = 8 360 60 1 = 360 6 120 1 = 360 3 45 1 = 360 8
total Area = 10 x 10 = 100 b2 1 trapezoid Area = ( )5(3 + 7) = 25 2 h 25 1 = P(falling inside the trapezoid) = b1 4 100 Area of a trapezoid formula 1 A = ( )h(b1 + b2) 2
1 triangle area = (8.66)(90) = 389.7 in2 2 circle area = л(8.66)2 = 235.6 in2 235.6 P(hitting circle) = 60.5 % = = 0.605 389.7 Area of a triangle Area of a circle 1 A = aP A = л r2 2 a = apothem (distance from the center to midpoint of a regular polygon)