Explanation:
the base of the pyramid has an area of b × h = 10 in × 5 in = 50 in²
a triangular face with a base of
10 inches has an area of (b×h)/2 = (10in×5.6in)/2 = 28in²
a triangular face with a base of
5 inches has an area of (b×h)/2 = (5in×7.1in)/2 = 17.75in²
the total surface is the sum of the rectangle plus the four triangles
50in² + 28in² + 28in² + 17.75in² + 17.75in² = 141.50in²