Even more free points for answers

A

Step-by-step explanation:

The area of a trapezoid is denoted by: , where and are the bases and h is the height.

Here, let's say that b1 is the top base and b2 is the bottom base. We know that the top base (b1) is 10 less than the height (h), so we can write:

b1 = h - 10

Plug this into the equation above:

Now, this area equation is actually equal to the area that the designers gave:

S = 4h² - 4h

So, we can set S equal to A:

Now solve for b2 in terms of h:

We see that b2 (the bottom base) is 2 inches longer than 7 times the height, which matches A.

Step-by-step explanation:

Area of a trapezoid:  

Step 1:  Find the area formula with the given instructions

The top base, a, is equal to 10 less than h.

a = h - 10

Set a to h-10 in the formula

Step 2:  Now we can evaluate both their equation and ours

Multiply both sides by 2

.

Divide both sides by h

Solve for b

 We now know that the bottom base, b, is 7 times the amount of h which is height plus 2.  This matches with the first option given.  Therefore, the answer for this question is OPTION A.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.