Question

question 1/ (5 points)
listen
what is the lateral area of the pyramid?
12.3 ft 11.9 ft
9 ft 11 ft
a) 103.3 ft.²
b) 289.2 ft.²
c) 125.7 ft.²
d) 241.6 ft.²

Explanation:

Step1: Recall the formula for lateral area of a pyramid

The lateral area \(L\) of a pyramid is the sum of the areas of its lateral faces. For a pyramid with a rectangular base of length \(l = 11\) ft and width \(w=9\) ft, and slant heights \(s_1 = 12.3\) ft and \(s_2 = 11.9\) ft. The formula for the lateral area of a rectangular - based pyramid is \(L=\frac{1}{2}(2l + 2w)s\) (where we can also calculate it as the sum of the areas of the four triangular faces: two triangles with base \(l\) and height \(s_1\), and two triangles with base \(w\) and height \(s_2\)). So \(L = 2\times(\frac{1}{2}\times l\times s_1)+2\times(\frac{1}{2}\times w\times s_2)\).

Step2: Substitute the values into the formula

Substitute \(l = 11\) ft, \(s_1=12.3\) ft, \(w = 9\) ft, and \(s_2 = 11.9\) ft into the formula.

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Answer:

D. \(241.6\mathrm{ft}^2\)