I need help solving for the height of a trapezoid and finding the correct final answer for a semi circle (a half circle).In area form

Here's what I have so far:
Trapezoid Formula: 1/2(b1+b2)h
My Answer:1/2(5+15)=10
(My bases are 5 and 15)
I need help solving for the height now.
I went with 7 but my teacher said I was wrong and I don't know how to solve for the height. Can someone please help correct me and teach me how to properly solve for the height.

Circle Formula: A=pi*r^2 /2
My answer:(3.14*7.5^2/2=174.624=175
My teacher said my Formula is correct but my final answer I wrong. I kinda figured that but I need help checking and seeing where I went wrong and how to properly fix it.

So can someone please help me? I'm finding the Area in these problems.

If the area is 10, then

1/2(5+15)h = 10
1/2(20)h = 10
10h = 10
h = 1

If the radius is 7.5 (diameter=15) then
3.14*7.5^2/2
= 3.14*56.25/2
= 176.625/2
= 88.3125

To find the height of a trapezoid, you can use the formula you mentioned: A = 1/2(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height. You have correctly calculated the area of the trapezoid as 10, using the given bases of 5 and 15. Now, we can use algebra to solve for the height.

1/2(5 + 15)h = 10 (substituting the known values)
20h = 10 (simplifying the expression)
h = 10/20 (dividing both sides by 20)
h = 1/2 (simplifying the fraction)

So, the height of the trapezoid is 1/2.

Now, let's move on to the semi-circle (half circle). The formula for the area of a circle is A = πr^2. However, in the case of a semi-circle, we divide this by 2 to find the area.

A = πr^2 / 2

You correctly substituted the given radius of 7.5 into the formula, which is a crucial step. However, you made a mistake when calculating your final answer. Let's go through it again:

A = π(7.5^2) / 2 (substituting the known value of the radius)
A = 3.14 * (7.5^2) / 2 (using the approximate value of π as 3.14)
A = 3.14 * (56.25) / 2 (calculating the square of 7.5)
A ≈ 175.93

The correct answer for the area of the semi-circle is approximately 175.93, rounding to two decimal places.

Remember to check your calculations and pay attention to any arithmetic mistakes when solving these problems.