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The area of a triangle is given by (1/2)*base*height. If the length of the sides becomes double so does the height. As base and height are becoming double the new area is 4 times the original area. What happens to the area of a parallelogram when the length of its base is doubled but the height remains the same?So if the base is doubled and height remains same, then the area doubles. What happens to the area of a triangle if the base is doubled? 1 Expert Answer The area will be the same as what you started with. Doubling the base doubles the area. Cutting the triangle in half cuts the area in half. How does the volume change if the height is doubled and the radius stays the same?Step-by-step explanation: So, if R = constant, the volume changes in direct proportion with the height. When the height doubles, the volume doubles. … A sphere with height h and radius r. How many times the area is changed when the sides of a triangle is doubled?Four times area is changed, when sides of a triangle are doubled. How does the area of an equilateral triangle change when the side length doubles? If every side of an equilateral triangle is doubled, the area of the new triangle is k times the area of the old one. What happens to the area of a parallelogram if the height doubles?The area of a parallelogram A = b × h. Hence, if a given height h doubles the result would be b × 2h = 2A, where A was the original area. If the height triples, the area would triple. What happens to the area of the parallelogram If the base becomes height and height becomes base?Alternative (ii) Remains the same is the correct answer to this question. If the base is increased 2 times and the height is halved then the area of the parallelogram Remains the same. When sides of triangle are doubled then its area? Step-by-step explanation: The area of a triangle is given by (1/2)*base*height. If the length ofthe sides becomes double so does the height. As base and height are becoming double the new area is 4 times the originalarea. When the length of the sides of a triangle double, thearea becomes quadruple. When each side of a triangle is doubled its area becomes?Answer: The area of the triangle is increased 4 times. What happens when you double the radius and height of a cylinder?In order to find the volume of a cylinder, you would use the formula V=3.14*r2*h. In the formula, the radius is being squared. That means that doubling the radius of the cylinder will quadruple the volume. What happens to the volume when you double the radius? The volume increased so much because, This makes the volume increase much faster than the radius.
D.the area is cut in half
Let's investigate the area of parallelograms some more. Exercise \(\PageIndex{1}\): A Parallelogram and Its Rectangles Elena and Tyler were finding the area of this parallelogram: Move the slider to see how Tyler did it: Move the slider to see how Elena did it: How are the two strategies for finding the area of a parallelogram the same? How they are different? Exercise \(\PageIndex{2}\): The Right Height? Study the examples and non-examples of bases and heights of parallelograms.
Are you ready for more? In the applet, the parallelogram is made of solid line segments, and the height and supporting lines are made of dashed line segments. A base b and corresponding height h are labeled. Exercise \(\PageIndex{3}\): Finding the Formula for Area of Parallelograms For each parallelogram:
In the last row, write an expression for the area of any parallelogram, using \(b\) and \(h\). Are you ready for more?
Here are two copies of the same parallelogram. On the left, the side that is the base is 6 units long. Its corresponding height is 4 units. On the right, the side that is the base is 5 units long. Its corresponding height is 4.8 units. For both, three different segments are shown to represent the height. We could draw in many more! No matter which side is chosen as the base, the area of the parallelogram is the product of that base and its corresponding height. We can check this: \(4\times 6=24\qquad\text{ and }\qquad 4.8\times 5=24\) We can see why this is true by decomposing and rearranging the parallelograms into rectangles. Notice that the side lengths of each rectangle are the base and height of the parallelogram. Even though the two rectangles have different side lengths, the products of the side lengths are equal, so they have the same area! And both rectangles have the same area as the parallelogram. We often use letters to stand for numbers. If \(b\) is base of a parallelogram (in units), and \(h\) is the corresponding height (in units), then the area of the parallelogram (in square units) is the product of these two numbers. \(b\cdot h\) Notice that we write the multiplication symbol with a small dot instead of a \(\times\) symbol. This is so that we don’t get confused about whether \(\times\) means multiply, or whether the letter \(x\) is standing in for a number. In high school, you will be able to prove that a perpendicular segment from a point on one side of a parallelogram to the opposite side will always have the same length. You can see this most easily when you draw a parallelogram on graph paper. For now, we will just use this as a fact.
Definition: base (of a parallelogram or triangle) We can choose any side of a parallelogram or triangle to be the shape’s base. Sometimes we use the word base to refer to the length of this side.
Definition: height (of a parallelogram or triangle) The height is the shortest distance from the base of the shape to the opposite side (for a parallelogram) or opposite vertex (for a triangle). We can show the height in more than one place, but it will always be perpendicular to the chosen base.
Definition: Parallelogram A parallelogram is a type of quadrilateral that has two pairs of parallel sides. Here are two examples of parallelograms.
Definition: Quadrilateral A quadrilateral is a type of polygon that has 4 sides. A rectangle is an example of a quadrilateral. A pentagon is not a quadrilateral, because it has 5 sides. |
What happens to the area of a parallelogram when the length of its base is doubled but the height remains the same?
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