Question

What is the lateral area of the pyramid?

Answer 1

We have two triangles with base 9ft and height 12.3ft and two triangles with base 11ft and height 11.9ft.

The formula of an area of a triangle:

$A_\triangle=\dfrac{1}{2}bh$

Triangle #1:

b = 9ft and h = 12.3ft. Substitute:

$A_1=\dfrac{1}{2}(9)(12.3)=55.35ft^2$

Triangle #2:

b = 11ft and h = 11.9ft. Substitute:

$A_2=\dfrac{1}{2}(11)(11.9)=65.45ft^2$

The Lateral Area:

$L.A.=2A_1+2_A2\\\\L.A.=2(55.35)+2(65.45)=241.6\ ft^2$

Answer: B. 241.6 ft².

Answer 2

Answer: B

Step-by-step explanation:

The point here, on calculating the Lateral Area of a Pyramid is searching for Congruent Triangles. In a rectangular pyramid, we have four triangles, in the Lateral Area.

The basic formula for calculating the Area of any triangle is:

Δ$=\frac{1}{2}*base*height$

So, let's plug it in the values for the 1st triangle:

Δ$\frac{1}{2}* 11*11.9$

Δarea=$65.45 ft^{2}$

For the second triangle (on the left):

Δ=$\frac{1}{2}*9*12.3=\\ 55.35 ft²$

The base is a rectangle, this assures us the base of the other faces is also 9 ft and 11 ft.

So we can assume the other Triangle are congruent to Triangle 1 and 2.

The Lateral Area is the sum of all Pyramid's Triangles area:

55.35+55.35+65.45+65.45=241.6 ft²