Given: abcd is a trapezoid, m∠b = 90º, m∠acd = 90º, ab = bc, ac = cd, ad = 12. find: area of abcd.

In Δ ACD:
m∠ACD = 90º  and  AC = CD   and     AD = 12
Δ ACD is isosceles right triangle and its hypotenuse is AD
∴ AC = CD = AD/√2 = 12/√2 = 6√2

in Δ ABC:
m∠B = 90º  and  AB = BC  and   AC = 6√2
Δ ABC is isosceles right triangle and its hypotenuse is AC
∴ AB = BC = AC/√2 = 6√2/√2 = 6

Area of ABCD = 0.5 (AD + BC) * AB = 0.5 *(6 +12) * 6 = 54

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

0.0078, 0.008, 0.077, 0.07