Two boards, one four inches wide and the other six inches wide, are nailed together to form an X. The angle at which they cross is 60 degrees. If this structure is painted and the boards are separated what is the area of the unpainted region on the four-inch board? (The holes caused by the nails are negligible.) Express your answer in simplest radical form.

The area of the unpainted region on the four inch board = 160·√3 in.²

Step-by-step explanation:

Here we have that the boards are crossing each other on their flat sides Therefore, when the boards are separated, the area of the unpainted region is the area of a parallelogram

The dimensions of the formed parallelogram are;

Interior angles = 60° and 120° (adjacent angles of a parallelogram)

Height, h of parallelogram formed = 4 inches

From the angle of crossing of the parallelogram, we have;

Angle between the width or perpendicular cross section of the 6 inches board and the angle of crossing of the two boards = 90° - 60° = 30°

Therefore, length of base, b of the parallelogram formed by the unpainted region is given as follows;

Therefore, the area of the parallelogram = b × h = 4 × 40·√3 = 160·√3 in.²

Hence, the area of the unpainted region on the four inch board = 160·√3 in.².

the answer is c. 23/3

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .