what is the surface area of this triangular pyramid? square yards

Explanation:

Step1: Calculate base - area

The base is a triangle with base $b = 52$ yd and height $h = 45$ yd. The area of a triangle is $A_{base}=\frac{1}{2}\times b\times h$. $A_{base}=\frac{1}{2}\times52\times45 = 1170$ square yards.

Step2: Calculate area of one of the three lateral - faces

The three lateral - faces are congruent triangles with base $b = 52$ yd and height $h = 63$ yd. The area of a triangle is $A_{lateral}=\frac{1}{2}\times b\times h$. $A_{lateral}=\frac{1}{2}\times52\times63 = 1638$ square yards.

Step3: Calculate total surface area

The total surface area $A$ of the triangular pyramid is the sum of the base - area and the areas of the three lateral - faces. $A=A_{base}+3\times A_{lateral}$. $A = 1170+3\times1638=1170 + 4914=6084$ square yards.

Answer:

6084