Part 1 is an online quiz - send me/show me your results
http://my.hrw.com/math06_07/nsmedia/practice_quizzes/geo/geo_pq_ffg_05.html
Part 2: What steps would you follow to complete this problem?
Find the area of the composite figure below formed by 2 identical three-quarter circles, 2 isosceles right triangles and a square.
In order to find the area of the composite figure, I must find the area of each shape that makes up the whole figure and add them all together.
ReplyDeleteFirst I would find the area of the two identical three-quarter circles. Since the square is 8cm, and it shows that the square cuts into the circle at 4, which is midway, that means the radius of the circle is 4. Now I find the area of the three-quarter circle by multiplying 16pi by 3/4. Now I know the area of the two three-quarter circles.
Next I find the area of the square by multiplying its length and width which are both 8.
Then I find the area of the smaller triangle which is equal to half of the area of the square.
Finally I find the area of the bigger triangle. It shows that a part of the side is 10cm, and the other part I know is 4cm because it is the radius of the three-fourths circle. So I add 10 and 4 together to get the length of each side. Multiply together and divide by two to get the area of the triangle.
Then I add all my results together to get the final answer. This is how I find the area of the composite figure.
I would find the area for each of the 2 identical three-quarter circles, 2 isosceles right triangles, and a square. For the 2 identical three-quarter circles, I would find the radius which is 8-4=4cm, then find the area which is 4*4*3.14, then multiply 3/4 since it is a three-quarter circle. I would then multiply it by two to find the area for two three-quarter circles.
ReplyDeleteFor the big right triangle, I would multiply base*base/2, and same for the little right triangle.
Next, for the square, it will be 8*8.
Finally, I would add all the areas for each shape, which will give me the area.
First, I will find the area of the smaller isosceles right triangle because I can figure out the height by knowing the width, 8 cm. Then, I will find the area of the square because I know that each side is 8 cm. Third, I will find the circles' area, using the equation of π × r2. I can know the length of the radius by subtracting 4 to 8. Then I will find the bigger triangle because I now know the measure of width and length by adding the radius length to 10. Finally, I will add them up and I will have the answer, the area of the composite figure.
ReplyDeleteSince the quadrilateral is a square, all the sides are 8 cm, and the area is 64 cm. And because one side of the square intersects the circle at 4 cm, that means the rest of the length, 4 cm, is the radius of the circle. With the radius, we can figure out that the area of the circle is 2 * 4 * 3.14, or 25.12 cm^2. However, 1/4 of the circle overlaps into the square so we need to subtract 1/4 of the area of the circle, which is 6.28 cm^2. 25.12 - 6.28 = 18.84 cm^2, the area of the three-quarter circle. This partial circle is identical to the other partial circle, which means it is also 18.84 cm^2. The smaller triangle has a leg of 8 cm, and the other leg is also 8 cm because the triangle is an isosceles. To find the area, we multiply the height, 8, by the width, 8, and divide by 2, giving us the answer, 32 cm^2. For the bigger triangle, the legs are divided into two parts. One part is 10 cm and the other part is the radius of the circle, 4 cm, giving a leg the total length of 14 cm. Because it is an isosceles, the other leg is also 14 cm. To find the area of the big triangle, we multiply the height, 14, by the width, 14, and divide by 2, giving us the answer, 98 cm^2. Finally, we add all the areas together: the two partial circles, the square, the small triangle, and the big triangle. 18.84 + 18.84 + 64 + 32 + 98 = 231.68 cm^2. The area of the composite figure is 231.68 cm^2.
ReplyDelete