Using Geometer’s Sketchpad to Find the Areas of Polygons



Using Geometer’s Sketchpad to Find the Areas and Perimeters of Polygons

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➢ Use the segment tool to draw a polygon.

➢ Use the select tool to go around your polygon and highlight all of the vertices. Be careful not to select any of the sides.

➢ Choose polygon interior from the construct menu. This fills the interior of the polygon.

➢ Select the interior (it will have a cross-hatch pattern).

➢ Choose area from the measure menu.

➢ Choose perimeter from the measure menu.

➢ Use the select tool to drag a vertex of your polygon. Notice how the area and perimeter change.

➢ Use the select tool to drag a side of your polygon. Notice how the area and perimeter change.

➢ Try to make a polygon with its area equal to its perimeter.

➢ Select the interior of the polygon.

➢ Choose a new color from the display menu. What happens of you choose other?

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Hold down the mouse button and drag to make one side of the polygon. Let up then quickly click again and drag to make the next side. Continue making sides until you are ready to close the polygon. As you drag the final side near the first vertex, the vertex turns blue. Let go of the mouse.

Draw a rectangle with area 60 cm2 and length 12cm. Use the segment tool to draw a diagonal of this rectangle. Construct the interior of one of the triangles. Color it blue. Construct the interior of the other triangle. Color it green. Find the area of each triangle.

➢ Open Sketchpad and choose show grid from the graph menu.

➢ Use the select (arrow) tool and highlight the x and y axes

➢ Choose hide axes from the display menu.

➢ Choose snap grid from the graph menu

Draw a polygon with vertices on the intersections of the grid lines. Use Pick’s Theorem to find the area and then use Sketchpad to find the area. Are they the same?

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Office for Mathematics, Science and Technology Education

mste.uiuc.edu

Office for Mathematics, Science and Technology Education

mste.uiuc.edu

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