How To Find Height Of Trapezium From Sides

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Suppose the surface area of the trapezoid is , with a superlative of and a base of . What must be the length of the other base?

Correct reply:

Caption:

Write the formula for finding the area of a trapezoid.

$A=\frac{h}{2}(b_1+b_2)$

Substitute the givens and solve for either base.

$30=\frac{10}{2}(5+b_2)$

30=5(5+b_2)

6=5+b_2

b_2=1

If the area of a trapezoid is , the height of the trapezoid is , and the base length is , what must be the length of the other base?

Right answer:

Caption:

Write the formula for the area of a trapezoid.

$A=\frac{h}{2}(b_1+b_2)$

Substitute all the given values and solve for the base.

$15=\frac{3}{2}(8+b_2)$

10=8+b_2

b_2=2

An isosceles trapezoid has base of operations measurements of and . The perimeter of the trapezoid is . Find the length for one of the two remaining sides.

Right answer:

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must take two nonparallel sides that have equivalent lengths. Since this problem provides the length for both of the bases as well as the total perimeter, the missing sides tin can be institute using the post-obit formula: Perimeter= Base 1 Base of operations two (leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

35=19+6+2(leg)

35=25+2(leg)

2(leg)=35-25

2(leg)=10
$leg=\frac{10}{2}=5$

Check the solution by plugging in the answer:

35=19+6+2(5)

35=25+10

35=35

An isosceles trapezoid has base measurements of and . Additionally, the isosceles trapezoid has a height of . Observe the length for i of the two missing sides.

Right answer:

$\sqrt{20}$

Explanation:

In social club to solve this problem, first annotation that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.

This problem provides the lengths for each of the bases too as the height of the isosceles trapezoid. In order to discover the length for one of the two equivalent nonparallel legs of the trapezoid, beginning utilize the height of the trapezoid to form right triangles on the interior of the trapezoid that each have a base length of . Run into image below:

Isos. trap intermediate geo
Annotation: the base length of can exist establish by subtracting the lengths of the two bases, then dividing that difference in half:

11-7=4

$4\div2=2$

Now, utilise the formula a^2+b^2=c^2 , where the length for ane of the ii equivalent nonparallel legs of the trapezoid.

Thus, the solution is:

2^2+4^2=c^2

4+16=c^2

20=c^2

$c=\sqrt{20}$

Isos. trap intermediate geo

The isosceles trapezoid shown above has base measurements of and . Additionally, the trapezoid has a height of . Detect the length of side .

Right answer:

$3\sqrt{26}$

Explanation:

In this trouble the lengths for each of the bases and the pinnacle of the isosceles trapezoid is provided in the question prompt. In guild to find the length for one of the two equivalent nonparallel legs of the trapezoid (side ), start apply the height of the trapezoid to form right triangles on the interior of the trapezoid that each accept a base length of.

The base of the interior triangles is equal to considering the difference between the two bases is equal to. And, this divergence must be divided evenly in one-half because the isosceles trapezoid is symmetric--due to the two equivalent nonparallel sides and the ii nonequivalent parallel bases.

Now, apply the pythagorean theorem: a^2+b^2=c^2 , where c=x .

3^2+15^2=c^2

9+225=c^2

c^2=234

$c=\sqrt{234}=\sqrt{9\times 26}=\sqrt{9}\sqrt{26}=3\sqrt{26}$

Thus, $x=3\sqrt{26}$

Isos. trap intermediate geo

Using the isosceles trapezoid shown above, find the length for one of the two nonparallel equivalent sides.

Right answer:

Explanation:

To solve this problem, first note that an isosceles trapezoid has 2 parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths. Since this trouble provides the length for both of the bases every bit well as the total perimeter, the missing sides can be constitute using the following formula: Perimeter= Base one Base of operations two(leg), where the length of "leg" is one of the two equivalent nonparallel sides.

Thus, the solution is:

39=17+8+2(leg)

39=25+2(leg)

2(leg)=39-25

2(leg)=14

$leg=\frac{14}{2}=7$

An isosceles trapezoid has ane base measurement of and the length for one of the nonparallel sides is. The perimeter of the trapezoid is 119 . Find the length for the other base of operations of the trapezoid.

Possible Answers:

Not plenty information is provided in this trouble.

Correct respond:

Caption:

To solve this problem, first annotation that an isosceles trapezoid has ii parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have ii nonparallel sides that have equivalent lengths.

Therefore, apply the given data to utilize the formula:

Perimeter= Base of operations 1 Base two(leg), where the length of "leg" is 1 of the two equivalent nonparallel sides.

Thus, the solution is:

119=45+2(24) +Base

119=48+45+Base

119=93+Base

Base=119-93=26

An isosceles trapezoid has base of operations measurements of and , respectively. Additionally, the isosceles trapezoid has a pinnacle that is $\frac{1}{3}$ the measurement of the larger base. Find the length for ane of the two equivalent nonparallel sides.

Right reply:

$\sqrt{26}$

Caption:

In lodge to solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have two nonparallel sides that have equivalent lengths.

This problem provides the lengths for each of the bases as well every bit informataion regarding the height of the isosceles trapezoid. In order to find the length for ane of the two equivalent nonparallel legs of the trapezoid, utilise the height of the trapezoid to class right triangles on the interior of the trapezoid that each accept a base length of. The interior triangle base of operations length of can exist found by subtracting the lengths of the 2 bases, then dividing that divergence in half:

15-13=2

$\frac{2}{2}=1$

In order to summate the exact height of the isosceles trapezoid (besides every bit the interior triangle), observe $\frac{1}{3}$ of the larger base. Since the largest base of the trapezoid is, the height of the trapezoid is: $\frac{1}{3}\times15=\frac{15}{3}=5$

At present you lot accept enough data to utilise the formula a^2+b^2=c^2 , where one of the missing sides.

The final solution is:

1^2+5^2=c^2

An isosceles trapezoid has base measurements of 115 and 163 . The perimeter of the trapezoid is 372 . Notice the length for one of the ii remaining sides.

Correct respond:

Explanation:

To solve this problem, first note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must have 2 nonparallel sides that have equivalent lengths. Since this trouble provides the length for both of the bases besides every bit the total perimeter, the missing sides tin can exist institute using the following formula: Perimeter= Base 1 Base ii(leg), where the length of "leg" is one of the 2 equivalent nonparallel sides.

Thus, the solution is:

372=163+115+2(leg)

372=278+2(leg)

2(leg)=372-278=94

$leg=\frac{94}{2}=47$

Cheque the solution by plugging in the answer:

372=163+115+2(47)
372=372

An isosceles trapezoid has ane base measurement of 100 and the length for one of the nonparallel sides is. The perimeter of the trapezoid is 301 . Find the length for the other base of the trapezoid.

Correct answer:

Caption:

To solve this problem, outset note that an isosceles trapezoid has two parallel bases that are nonequivalent in length. Additionally, an isosceles trapezoid must accept ii nonparallel sides that have equivalent lengths.

Therefore, use the given information to employ the formula:

Perimeter= Base one Base two(leg), where the length of "leg" is ane of the two equivalent nonparallel sides.

Thus, the solution is:

301=100+2(55) +Base

301=100+110+Base

301=210+Base

Base=301-210=91

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