WILL GIVE BRAINLIEST, please explain your answer! Calculate the area of the block "V" shown below. *Drawing not to scale

  132 mm^2

Step-by-step explanation:

The line added to the figure in the attachment shows it can be divided into two figures whose area is easily calculated.

  1. A parallelogram of base length 20 mm and height 4 mm:

     A = bh = (20 mm)(4 mm) = 80 mm^2

  2. A trapezoid with bases 32 mm and 20 mm, and height 2 mm:

     A = (1/2)(b1 +b2)h = (1/2)(32 mm +20 mm)(2 mm) = 52 mm^2

The total area of the figure is then ...

  80 mm^2 +52 mm^2 = 132 mm^2

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240