What is the total surface area of the solid?

A rectangular prism with a length of 16 millimeters, width of 11 millimeters, and height of 10 millimeters. A triangular prism with a triangular base with a base of 11 millimeters and height of 8 millimeters. The prism has a height of 16 millimeters.

Step-by-step explanation:

The formula for determining the total surface area of a rectangular prism is expressed as

Total surface area = 2lw + 2wh + 2lh

Where

l represents the length = 16

w represents the width = 11

h represents the height = 10

Total surface area = (2 × 16 × 11) + (2 × 11 × 10) + (2 × 16 × 10) = 352 + 220 + 320 = 892 mm²

The formula for determining the total surface area of a triangular prism is expressed as

Total surface area = ph + 2b

p represents perimeter of base

h represents height of prism

b represents base area

From the information given,

h = 16

b = 1/2base × height = 1/2 × 11 × 8 = 44 mm²

to determine the perimeter of the base, we would determine the slant height, l by applying Pythagoras theorem.

Hypotenuse² = opposite side² + adjacent side²

l² = 11² + 8² = 185

l = √185 = 13.6

p = 13.6 + 11 + 8 = 32.6 mm

Total surface area = (32.6 × 16) + (2 × 44) = 521.6 + 88 = 609.6 mm²

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