Answer:
A) 15 cm
B) 1240 cm²
Step-by-step explanation:
Part A: The height of the triangular base can be found a couple of ways. One is to use the Pythagorean theorem.
The triangular base is isosceles, so the height, half its base (8 cm) and the long edge (17 cm) form a right triangle. The height is then found from ...
17² = 8² + height²
289 -64 = height² . . . . . subtract 64
√225 = 15 = height . . . . take the square root
The height of the triangular base is 15 cm.
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Part B: The volume of a prism is given by ...
V = Bh
where B is the area of the base and h is the length ("heigh") of the prism. We can use this formula to find B, the area of each of the triangular bases of the prism.
2400 cm³ = B·(20 cm)
2400 cm³/(20 cm) = B = 120 cm² . . . . . area of one end of the prism
Now the lateral area of the prism is the product of its length (20 cm) and the perimeter of its base (17 cm + 17 cm + 16 cm). That area is ...
lateral area = (20 cm)(50 cm) = 1000 cm²
Together with the areas of the two ends, we find the total area of the cardboard box to be ...
total area = lateral area + 2×base area = 1000 cm² + 2×120 cm²
total area = 1240 cm²
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Note that you can also find the <em>height of the base triangle</em> from the base area.
A = (1/2)bh
120 cm² = (1/2)(16 cm)h
120 cm²/(8 cm) = <em>h = 15 cm</em>
