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The area of a trapezoid is found by using the equation , where h is the height and b1 and b2 are the lengths of the bases. What is the area of the trapezoid shown below?
  • a)
    18
  • b)
    20
  • c)
    24
  • d)
    30
  • e)
    36
Correct answer is option 'E'. Can you explain this answer?
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The area of a trapezoid is found by using the equation , where h is th...
To solve this problem, first determine the length of the top base using the Pythagorean theorem. Since the height is 4 and the length of one of the diagonal sides is 3, the length of the other leg of the triangle is 3. The top base equals the length of the bottom base plus twice the leg of the triangle just calculated. Thus the length of the top base is 6 + 2(3) = 12. Using the formula for the area of a trapezoid,  (6 + 12), or 36.
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Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so. Study 1A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.Study 2The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.In Study 1, which medium tested had the greatest density?

Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so. Study 1A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.Study 2The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.According to Study 2, water at which of the following temperatures yields the greatest velocity of sound?

Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so. Study 1A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.Study 2The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.According to the data in Study 1, as density increases, what happens to the velocity of sound?

Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so. Study 1A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.Study 2The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.According to Study 2, over what temperature interval does velocity begin to decrease as water temperature rises?

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The area of a trapezoid is found by using the equation , where h is the height and b1 and b2 are the lengths of the bases. What is the area of the trapezoid shown below?a)18b)20c)24d)30e)36Correct answer is option 'E'. Can you explain this answer?
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