Question

15 yd
16 yd
16 yd
area of u =
area of v =
area of w =
area of x =
area of y =
surface area =

Explanation:

Step1: Analyze the shape (square base and triangular faces)

The base (W) is a square with side \( s = 16 \) yd. The triangular faces (U, V, X, Y) are congruent triangles with base \( b = 16 \) yd and height \( h = 15 \) yd.

Step2: Calculate Area of W (square)

The area of a square is \( A = s^2 \). For \( s = 16 \) yd, \( A_W = 16^2 = 256 \) square yards.

Step3: Calculate Area of one triangular face (e.g., U, V, X, Y)

The area of a triangle is \( A = \frac{1}{2}bh \). For \( b = 16 \) yd and \( h = 15 \) yd, \( A_{\text{triangle}} = \frac{1}{2} \times 16 \times 15 = 120 \) square yards. Since U, V, X, Y are congruent, their areas are all 120.

Step4: Calculate Surface Area

Surface Area = Area of W + Area of U + Area of V + Area of X + Area of Y = \( 256 + 120 + 120 + 120 + 120 \)
= \( 256 + 4 \times 120 = 256 + 480 = 736 \) square yards.

Answer:

Area of U = 120 square yards
Area of V = 120 square yards
Area of W = 256 square yards
Area of X = 120 square yards
Area of Y = 120 square yards
Surface Area = 736 square yards