Question

jeremy constructed this solid by combining two rectangular prisms and a square pyramid. what is the surface area of this figure? square meters

Explanation:

Step1: Calculate the area of each face

• Left - most rectangle: Area \(A_1 = 2\times6= 12\)
• Middle - left parallelogram: Area \(A_2=8\times6 = 48\)
• Middle - middle rectangle: Area \(A_3=3\times6=18\)
• Middle - right triangle: Area \(A_4=\frac{1}{2}\times6\times7 = 21\)
• Bottom - left parallelogram: Area \(A_5 = 14\times6=84\)
• Bottom - middle rectangle: Area \(A_6=5\times6 = 30\)
• Bottom - right triangle: Area \(A_7=\frac{1}{2}\times6\times6=18\)
• Back - side:
• For the left - part (rectangle and parallelogram combination): \(2\times14+8\times14=(2 + 8)\times14=140\)
• Middle - part (rectangle): \(3\times14 = 42\)
• Right - part (two triangles): \((\frac{1}{2}\times6\times7+\frac{1}{2}\times6\times6)\times2=(21 + 18)\times2=78\)

Step2: Sum up all areas

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Answer:

322 square meters