9514 1404 393
Answer:
n cm = 3 cm
Explanation:
The total surface area is the sum of the base areas and the lateral area. The base areas are the sum of the areas of the rectangle and triangle that define the shape of the base.
The rectangle has dimensions 5 cm by n cm. The triangle is 5-2 = 3 cm high and 4 cm at the base. Then the front face area is ...
A = lw + 1/2bh
A = (5 cm)(n cm) +1/2(4 cm)(3 cm) = (6 +5n) cm²
The lateral area is the product of the perimeter of the base and the depth of the prism.
A = Ph
A = (5 cm + n cm + 2 cm + 5 cm + 4 cm + n cm)(4 cm) = (64 +8n) cm²
The total surface area is the sum of the areas of the two bases and the lateral area:
130 cm² = 2(6 +5n) cm² +(64 +8n) cm²
130 = 76 +18n . . . . . . divide by cm², collect terms
54 = 18n . . . . . . . . . subtract 76
3 = n . . . . . . . . . . divide by 3
The value of n in centimeters is 3 cm.