A patio is to be made in the shape of an isosceles triangle as shown. (a) Why would the calculation A= 1/2 (22) (16) not result in the correct area of the triangle?
(b) Determine the area of the patio to the nearest square foot.
(c) If the patio is to be covered by stone that costs $12.25 per square foot, what will be the total cost of covering the patio with stone?

9514 1404 393

  (a) 22 is not the correct value of h

  (b) 164 ft²

  (c) $2009

Step-by-step explanation:

(a) Apparently, the formula ...

  A = 1/2bh

was used. We recognize the base of the triangle is 16 feet, so apparently the formula was used with h=22.

22 is the side length, not the perpendicular distance from the base to the opposite vertex.

The computed value is not the area because 22 is not the height.

__

(b) Given three side lengths, an appropriate formula is Heron's formula:

  s = (a+b+c)/2 and A = √(s(s-a)(s-b)(s-c))

Here, we have ...

  s = (22 +22 +16)/2 = 30  and  A = √(30(8)(8)(14) = 16√105 ≈ 163.95

The area is about 164 square feet.

__

(c) At $12.25 per square foot, the cost of materials will be ...

  (164 ft²)($12.25/ft²) = $2009

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.