Learning Intentions: Students will develop an understanding of how trapezoids and kites can be decomposed into simpler shapes in order to calculate their area.
Monday, March 25, 2019
Day 130: Area of Trapezoids and Kites
Math 6 and Math 6+ students worked with calculating the area of trapezoids and kites today in class. The lesson began with analyzing these two shapes on grid paper in an attempt to develop a formula that could be used to determine how to calculate their area. Students worked with decomposing, breaking down the shapes, to help with the process. We also added on shapes in an attempt to construct rectangles to aid in the decision making.
Learning Intentions: Students will develop an understanding of how trapezoids and kites can be decomposed into simpler shapes in order to calculate their area.
Learning Intentions: Students will develop an understanding of how trapezoids and kites can be decomposed into simpler shapes in order to calculate their area.
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It makes sense because you have to take to average of the first base times the height and the average of the second base times the height. To get the average, you would add them both up and then divide them by 2. Then you would multiply it by the heighth.
ReplyDeleteThe equation for a trapezoid makes sense because you are taking the area of the rectangle inside the trapezoid, and what the trapezoid could be if you expanded the borders so it were a rectangle, and averaging it. The rectangle inside is already part of the trapezoid, and if you are expanding the borders of the trapezoid, you are making it have a larger area than it should be. You have to take the difference between the larger rectangle and the smaller one, and because the part of the trapezoid is only making half of that difference, you would split that in half. It would be exactly in between the larger and smaller sized rectangles. (It is really hard to explain what is going on inside my brain)
ReplyDelete(B+B)h*1/2 is the formula for a trapezoid. It works because the area of a trapezoid is also the average of the smallest base times height and the largest base times height.
ReplyDeleteThe formula to find the area of a trapezoid works because you still get the right answer but have much less work to do.
ReplyDeleteTo find the area of a trapezoid you would do base 1 plus base 2 then multiply that by the height. Then you would divide it by 2 to get the area. You would do that because the triangles are half of a square or rectangle and that is why you would divide it by 2. You would use both bases because they are parallel lines but have different measurements.
ReplyDeleteThe formula to finding the area of a trapezoid works because you must find the average. There are 2 bases, base one and base two. Base one (which is typically the smaller length) is multiplied by the height to get a small rectangle inside the trapezoid, the larger base and the height create a large rectangle. The triangle(s) will probably be half of it's own mini rectangle. And the distance between the mini rectangle(s) and the rectangle in the middle is the average. So, it's formula would be h(b1 + b2) * .5 = the area.
ReplyDeleteI think that this algorithm works because since a trapezoid can be divided up into different shapes but still be able to use the same base. After you find what both the equations equal then you have to divide the sum by 2 because you divided the shape before.
ReplyDeleteThe algorithm works, because the two triangles outside of the rectangle in the center reclaims half of the area on the left hand side and half the area on the right hand side.
ReplyDeleteI think that the formula for a trapezoid (b1 + b2)h * 1/2 works because trapezoid can be divided up into different shapes but still be able to use the same base. After you find what both the equations equal then you have to divide the sum by 2 because you divided the shape before.
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