Answer:
A: 15 cm
B: 1120 cm²
Step-by-step explanation:
<u>Part A</u>: The triangle is isosceles, so its altitude bisects the base, giving two right triangles with hypotenuse 17 and leg 8. Then the other leg can be found from the Pythagorean theorem:
h² +8² = 17²
h = √(289 -65) = 15
The height of the base is 15 cm.
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<u>Part B</u>: The total surface area of the prism is the sum of the lateral area and the areas of the triangular bases.
Base area = (1/2)(b)(h) = (1/2)(8 cm)(15 cm) = 60 cm²
The lateral area is the product of the perimeter of the base and the length of the prism:
LA = PL = (17 cm +17 cm +16 cm)(20 cm) = 1000 cm²
So, the total surface area of the box is ...
2(base area) + lateral area = 2(60 cm²) +1000 cm² = 1120 cm²
The box uses about 1120 cm² of cardboard.
