Can someone me with this geometry problem, ?

Hello from MrBillDoesMath!

72

Discussion:

Total Surface area = area of pyramid base + 4 ( area of triangular face)

In our case this becomes

                                 4*4                               + 4(  (1/2) (4)(7) )  =

                                 = 16 + (2)(4)(7)

                                 = 16 + 56        

                                 = 72

which is the first choice.  

Note: the area of a triangular face was computed using (1/2) b h, which in our case is

(1/2) (4) (7)

Thank you,

MrB

your answer is -9

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true