What is the surface area of the pyramid? 110 square units

166 square units

280 square units

312 square units

*See attachment for the pyramid being referred to here

166 square unit

Step-by-step explanation:

==>Given:

From the attachment, we are given the 2-dimensional diagram of the 3-dimensional diagram of the pyramid showing the dimensions of each faces as follows:

2 triangular faces=> base (b) = 2; height (h) = 13

2 triangular faces=> base (b) = 10; height (h) = 12

1 rectangular face=> length (l) = 10; width (w) = 2

==>Required:

Surface area of the pyramid = sum of area of all the faces

==>Solution:

Sum of surface area of all the faces = area of the 4 triangular faces + area of rectangular face

=>Area of the first 2 similar triangles with b = 2, h = 13 would be 2*(½bh)

= 2*(½*2*13)

= 2*(13)

= 26 square unit

==>area of the second set of 2 similar triangular faces with b = 10, h = 12 would be 2*(½bh)

= 2*(½*10*12)

= 2*(60)

= 120 square unit

==>Are of the rectangular face with l = 10, w = 2 would be l × w:

Area = 10 × 2 = 20 square unit

Total surface area of the pyramid = 26 + 120 + 20 = 166 square unit