Find the area enclosed by the figure where a = 15 ft, b = 45 ft, c = 20 ft, d = 75 ft, and f = 40 ft.

If a, b , etc are sides of a pentagon, then we don't have enough information, since the figure is not "rigid"

Did you have some angles given?

show that points (3,-1) (4,2) (1,3) and (-2,-1) the vertices kite-shaped quadrilateral find its area

To find the area enclosed by the figure, we need to determine the shape of the figure and then calculate its area using the appropriate formula.

Given the values of a, b, c, d, and f, we can identify that the figure is a trapezoid. A trapezoid is a quadrilateral with one pair of parallel sides.

To determine the area of a trapezoid, we can use the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

In this case, the length of the parallel sides can be determined by the given values as follows:

a = 15 ft
b = 45 ft

The height of the trapezoid can be calculated using the given values of d and f. Since d and f are the lengths of the two non-parallel sides, the height is the perpendicular distance between these two sides.

To calculate the height, we can use the Pythagorean theorem:

h = sqrt(d^2 - f^2)

Substituting the given values in the formula:

h = sqrt(75^2 - 40^2) = sqrt(5625 - 1600) = sqrt(4025) ≈ 63.43 ft (rounded to two decimal places)

Now we have the values for a, b, and h, we can substitute them into the area formula:

Area = (a + b) * h / 2
Area = (15 + 45) * 63.43 / 2
Area = 60 * 63.43 / 2
Area ≈ 1902.9 ft² (rounded to one decimal place)

Therefore, the area enclosed by the figure is approximately 1902.9 square feet.