Question

question 13 of 25
what is the surface area of the regular pyramid given below?
a. 140 units²
b. 329 units²
c. 189 units²
d. 280 units²

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 7\). The area of a square \(A_{base}=s^{2}\), so \(A_{base}=7\times7 = 49\)

Step2: Calculate the lateral - face area

The lateral faces are 4 congruent triangles. The base of each triangle is \(b = 7\) and the height (slant height) \(h\) of each triangle is \(10\). The area of a triangle \(A_{\triangle}=\frac{1}{2}\times b\times h\). For one triangle: \(A_{\triangle}=\frac{1}{2}\times7\times10=35\). For 4 triangles: \(A_{lateral}=4\times35 = 140\)

Step3: Calculate the total surface area

The surface area of a pyramid \(A = A_{base}+A_{lateral}\). Substitute \(A_{base}=49\) and \(A_{lateral}=140\) into the formula: \(A=49 + 140=189\)

Answer:

C. 189 units²