+36 This image shows a square pyramid.
What is the surface area of this square pyramid?
A. 36ft^2
B. 72ft^2
C. 78ft^2
D. 84ft^2
+23246 The area of the base is 6 x 6 = 36.
Since the left-hand triangle of the front side is a 45-45-90 triangle, the length of the dotted line segment (the height) of the front triangle is equal to the distance from the left-hand corner dot to the middle dot of the front side.
Because the length of the base of the front side is 6, the distance from the left-hand corner dot to the middle dot is 3; therefore, the length of the height of the front side is also 3.
The area of the front side is 1/2 x base x height = 1/2 x 6 x 3 = 9.
The total area = (area of the base) + 4 x (area of the front side) = (36) + 4 x (9) = 72 square feet.
+9519 \(\text{Slant height}=\dfrac{\frac{6}{2}}{\sin45^{\circ}}=3\sqrt2\\ \text{Surface area} = 6^2 + 4\times \dfrac{1}{2}\times 6\times 3\sqrt2\times \sin45^{\circ}\\ \qquad\qquad\;\;\;\;\;\!\;\;\!\!=36 + 36 \\\qquad\qquad\;\;\;\;\;\!\;\;\!\!=72\)
Area of any triangle: a and b are 2 side lengths of the triangle and C is the included angle of a and b, then area = \(\dfrac{ab\sin C}{2}\).
