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What is the height and bases of a trapezoid where one base is twice the other and the height is the average of the two bases the area is 324?
Area of the trapezoid: A = (1/2)(B + b)(h)
Let b =x, then B = 2x, and h = (2x + x)/2.
Substitute what is given in the formula, and we have:
A = (1/2)(B + b)(h)
324 = (1/2)(2x + x)[(2x + x)/2]
324 = (1/4)(3x)(3x)
324 = (1/4)(9x^2)
324 = (9/4)x^2 multiply by 4/9 to both sides
1296/9 = x^2
144 = x^2
12 = x (since the length is positive, ignore negative value for x)
2x = 2 x 12 = 24
(2x + x)/2 = (24 + 12)/2 = 36/2 = 18
Thus, the small base is 12, the big base is 24, and the height is 18.
What else can I help you with?
What shapes make a trapezoid?
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. The bases can be of different lengths, but they must be parallel to each other. The angles formed by the bases and the legs of a trapezoid can vary in size.
An isosceles trapezoid is a trapezoid with congruent bases?
False.
Does a trapezoid have one or more pairs of parallel sides?
A trapezoid is a quadrilateral with at least one pair of parallel sides. This pair of parallel sides are known as the bases of the trapezoid. The other two sides are called the legs, and they are not parallel to each other. So, a trapezoid has exactly one pair of parallel sides.
Do the diagonals of a trapezoid bisect each other?
No, never. A trapezoid may have diagonals of equal length (isosceles trapezoid), but they do not intersect at their midpoints.Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. But this is a contradiction since the respective bases of the triangles, forming the top and bottom of the trapezoid are, of course, not equal. Therefore, the triangles cannot be congruent. Hence, we have given proof by contradiction that diagonals in a trapezoid cannot bisect each other.
What are two other names for a trapezoid?
A trapezoid is called a trapezium in the UK (because the UK trapezoid is scalene). In any case, a trapezoid is also a quadrilateral, in that it has four sides.
What is the area of a trapezoid if the meausure of the base is 8 and the height is 5?
Area of a trapezoid = 0.5*(sum of parallel bases)*height Need to know the measure of the other base
What are the bases on the trapezoid?
The bases on a trapezoid are the two lines that are parallel to each other. .............................. ....____base____...... .../ ...................\..... ../ .....................\.... ./_____base_____\... .............................
When figuring out the area of a trapezoid what does b2 mean?
In the formula for the area of a trapezoid, ( A = \frac{1}{2} (b_1 + b_2) h ), ( b_2 ) represents the length of one of the two parallel sides (bases) of the trapezoid. The other base is denoted as ( b_1 ). The height ( h ) is the perpendicular distance between these two bases. The area is calculated by averaging the lengths of the bases and then multiplying by the height.
What is the area of a trapezoid with the height of 12cm and the base of 15 cm?
The formula to calculate the area of a trapezoid is (1/2) * sum of the bases * height. Given that the height is 12 cm and the bases are 15 cm and another side, the area can be calculated as (1/2) * (15 + b) * 12, where b is the length of the other base.
What is the area of trapezoid with bases 8 inch and 12.5 inches and the height of 6 inches?
The area of any trapezoid is 1/2 times (length of one base plus length of the other base) times (height). You ought to be able to handle it from there.
Is an isosceles trapezoid has congruent bases?
No. The other two sides are congruent.
One base of a trapezoid is three times as long as the other the height is the average of the two bases if the area of the trapezoid is 112yd find the length of the longer base?
Let the shorter base be ( b ) and the longer base be ( 3b ). The height is given as the average of the two bases, which is ( \frac{b + 3b}{2} = 2b ). The area of the trapezoid is given by the formula ( \text{Area} = \frac{1}{2} \times (b + 3b) \times \text{height} ), leading to ( 112 = \frac{1}{2} \times 4b \times 2b ). Simplifying gives ( 112 = 4b^2 ), so ( b^2 = 28 ) and ( b = \sqrt{28} = 2\sqrt{7} ). Therefore, the longer base is ( 3b = 6\sqrt{7} ) yards.
HAs only one pair of parallel sides?
A trapezoid has only one pair of parallel sides. These parallel sides are called the bases of the trapezoid, while the other two sides are non-parallel and are known as the legs of the trapezoid.
What are all parts of a trapezoid?
Two bases that are parallel to each other and two sides that are of unequal lengths unless it is an isosceles trapezoid whereas the sides will be equal in length.
Can any side of a trapezoid be called a base?
No, only the two sides that are parallel to each other are bases.
What is the area of a trapezoid with base lengths 14 cm and 12 cm and a height of 8 cm?
The area of ANY trapezoid is [ 1/2 times (height) times (one base plus the other base) ].Knowing that, you can now find the area of not only that particular trapezoid, but ofevery trapezoid that you ever encounter for the rest of your life. The formula is notexpected to change. You are empowered !
Can any side of a trapezoid can be called a base?
The two parallel sides are called the bases, and the two non-parallel sides are the legs. If you call any other pair of sides the bases, the formula for the area of the trapezoid will no longer work.
