Unknown Area Problems on the Coordinate Plane – Practice Problems

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A composite shape is an irregularly-shaped figure that can be broken up into simpler, more basic shapes like rectangles, squares, triangles, trapezoids, circles, or even half circles. The area refers to the number of square units that can fit in the region bounded by the composite shape. To compute for its area on a coordinate plane, first, split up the composite shape into non-overlapping basic shapes and identify the x and y coordinates of all relevant vertices if the basic shape is a polygon or the endpoints of a diameter if the basic shape is a circle or a half circle. Then, find the area of each individual basic shape by evaluating the appropriate area formula and computing for the necessary dimensions based on the coordinates. Finally, compute for the area of the composite shape by combining the areas of the individual basic shapes and get the actual area of the foundation by multiplying the resulting area on the coordinate plane by the corresponding scale factor. Learn how to determine the area of composite shapes on a coordinate plane by helping Mr. Tad Dunlop, a real estate tycoon, and his construction site manager interpret the architect’s building plan for the foundations of two new skyscrapers in Grid City. Common Core Reference: CCSS.MATH.CONTENT.6.G.A.3

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Exercises in this Practice Problem
Explain how to calculate the area of a composite shape on a coordinate plane.
Determine the area of the composite shape.
Determine the area of the new amusement park.
Find the errors in the calculations for the area of the composite shapes.
Find the formulas for the different shapes.
Determine how expensive the new school’s playground is going to be.