What is the total surface area of the figure shown?

Surface area of the figure = 1000 in²

Step-by-step explanation:

From the figure attached,

Two rectangular prisms A and B have been shown with the dimensions.

Surface area of a rectangular prism = 2(length + width) × height

Surface area of prism A = 2(9 + 10) × 20

                                        = 760 in²

Surface area of prism B = 2(15 + 10) × 8

                                        = 16×25

                                        = 400 in²

But one surface of prism B along the width and the same area of prism A are hidden.

Area of the hidden surfaces = 2(10 × 8)

                                               = 160 in²

Total surface area of the figure = 760 + 400 - 160

                                                    = 1000 in²

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.