What area is this shape ?

9514 1404 393

  40 square units

Step-by-step explanation:

The area can be considered as that of two trapezoids, a rectangle, and a triangle. The total area is the sum of the areas of these.

Draw two horizontal lines, one beginning at the left-most point, and another 2 units below that. Draw a vertical line segment extending the vertical line at the top down to the first horizontal line. Now the figure is divided as described above.

The upper left trapezoid has bases of 3 and 5, and a height of 4. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(3 +5)(4) = 16

The trapezoid between the two horizontal lines has bases of 8 and 7, and a height of 2. Its area is ...

  A = (1/2)(8 +7)(2) = 15

The rectangle at upper right has a base of 2 and a height of 3. Its area is ...

  A = bh

  A = 2(3) = 6

The triangle at the bottom has a base of 3 and a height of 2. Its area is ...

  A = 1/2bh

  A = 1/2(3)(2) = 3

Then the total area of all of these pieces is ...

  Area = 16 +15 +6 +3 = 40 . . . . square units

the answer is 40 square units

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

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