Find the height and base of a trapezium

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In summary, the conversation discussed problem #5 and #6, both involving finding the length of a missing side in a right triangle. In problem #5, the missing side x was found to be approximately 6.9 inches using the Pythagorean theorem. In problem #6, the length of x was determined to be 20.9 feet by dividing it into three portions and using the Pythagorean theorem on the two right triangles. There was confusion about the shorter length of the triangle on the right, which was resolved by correctly using the Pythagorean theorem.
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Etrujillo
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To start with problem #5 i cut the shape
Into 2, a triangle and a square, i know that the additional leg length to the triangle can be found by subtracting base 1 and base 2=4 so i have a triangle with a hypotenuse of 8 inches, 1 leg=4 and now i have to find the length of the other leg. The length of the other leg can be found by multiplying the length of the other leg by the square root of 3 to get (4×3squared)=6.9282 the area for that triangle would be 13.84. Now i have to find the missing side of x. It seems to be a rectangle, and i know the formula for that is length×width to get the area but i noticed a squared angle in the right bottom. Thats where i get lost. As for #6, i can start with finding out the missing leg of the triangle on the left which is half of its hypotenuse so i would divide 7÷2=3.5 then id get started with calculating the shorter length of the triangle on the right which would be half its length of hypotenuse to 8÷2=4 what i think i would do next is add 3.5+4+12= 19.5 as the value of x. Can anyone please verify if I am right? If not what did i do wrong?. Thank you

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In problem 5, the side marked "x" is a leg of a right triangle with hypotenuse of length 8 in and the other leg of length 14- 10= 4 in. Using the Pythagorean theorem, [tex]8^2= 64= 4^2+ x^2= 16+ x^2[/tex] so [tex]x^2= 64- 16= 48[/tex]. [tex]x= \sqrt{48}= 4\sqrt{3}[/tex] which is approximately 6.9 in. I am not sure why you then calculate areas. The problem posted only asks for the length x.

In problem 6, divide the side marked "x" into three portions by drawing perpendiculars from the upper vertices to the base. The leftmost portion is a leg of a right triangle with hypotenuse of length 7 ft and the other leg of length 6 ft. Use the Pythagorean theorem to get [tex]\sqrt{49- 36}= \sqrt{13}[/tex] which is 3.6 to one decimal place. The middle portion has length the same as the top edge, 12 ft, and the right portion is one leg of a right triangle with hypotenuse of length 8 ft and one leg of length 6 ft. The right portion has length [tex]\sqrt{64- 36}= \sqrt{28}= 2\sqrt{7}[/tex] which is 5.3 to one decimal place. x= 3.6+ 12+ 5.3= 20.9 ft.

I don't know why you think that "the shorter length of the triangle on the right which would be half its length of hypotenuse". Where did you get that idea?
 
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1. What is a trapezium?

A trapezium is a quadrilateral shape with only one pair of parallel sides. It is sometimes referred to as a trapezoid.

2. How do you find the height of a trapezium?

To find the height of a trapezium, you can use the formula: h = (2 * area) / (a + b), where h is the height, area is the area of the trapezium, and a and b are the lengths of the parallel sides.

3. How do you find the base of a trapezium?

The base of a trapezium is one of the parallel sides. To find the base, you can measure it directly or use the formula: b = (2 * area) / (h + a), where b is the base, area is the area of the trapezium, h is the height, and a is the length of the other parallel side.

4. Can you find the height and base of a trapezium if you only know the area?

Yes, you can find the height and base of a trapezium if you know the area. You can use the formulas mentioned above, or you can use the formula: area = (1/2) * (a + b) * h, where area is the area of the trapezium, a and b are the lengths of the parallel sides, and h is the height.

5. Is there a specific unit of measurement for the height and base of a trapezium?

The unit of measurement for the height and base of a trapezium will depend on the unit used for the other measurements, such as the lengths of the sides or the area. It is important to use the same unit of measurement for all values in the calculations to get an accurate result.

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