Question

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?

Answer 1

9514 1404 393

Answer:

(a) 22 is not the correct value of h

(b) 164 ft²

(c) $2009

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.

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(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.

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

(164 ft²)($12.25/ft²) = $2009