Question

Can someone give me a detailed explanation on hypotenuse and pythagoreas theorem and how you can use it in a trapezium. You can use pictures and other attachments also.

Thanks so much!

Answer 1

I hope it will help you

What is the length of the diagonals of trapezoid ABCD?

Assume the figure is an isoceles trapezoid.

Explanation:
To find the length of the diagonal, we need to use the Pythagorean Theorem.

Therefore, we need to sketch the following triangle within trapezoid ABCD:

We know that the base of the triangle has length 9m.

By subtracting the top of the trapezoid from the bottom of the trapezoid, we get:

12m−6m=6m

Dividing by two, we have the length of each additional side on the bottom of the trapezoid:

6m2=3m

Adding these two values together, we get 9m.

The formula for the length of diagonal AC uses the Pythagoreon Theorem:

AC2=AE2+EC2, where E is the point between A and D representing the base of the triangle.

Plugging in our values, we get:

AC2=(9m)2+(4m)2

AC2=81m2+16m2

AC2=97m2

AC=√97m

Hope this will help you

Pls mark as a brainlist

See the 2 diagram in pics

Answer 2

The hypotenuse is the longest side in a right triangle.
The Pythagoras' theorem.
This theorem states that in a right triangle, the sum of squares of the two legs is equal to the square of the hypotenuse.
${a}^{2} + {b}^{2} = {c}^{2}$
Where, c is the hypotenuse, a and b are the two legs.

Let's tale a trapezium whose parallel sides are of length 10units and 16units and non- parallel sides are of length 5 units. Let's calculate the height of the trapezium.
Drop an altitude from the opposite vertex to draw the height. Now, the longer side= 10u+ 2x=16units
x=3 u. x is the base of the right triangle that we just formed.
Applying Pythagoras' theorem,
${a}^{2} + {b}^{2} = {c}^{2}$
3u^2+ height^2=5^2 u^2
9u^2+height^2 = 25 u^2
height^2 =25-9 u^2
height^2 =16 u^2
height=√16 u^2
height =4u.

Therefore, the height of the trapezium is 4units.