Question

A patio is to be made in the shape of an isosceles triangle as shown.

Answer 1

9514 1404 393

Answer:

  (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