Answer:
a. 84 cm² b. The area of the polyhedron is found by finding the sum of the areas of each individual shape.
Step-by-step explanation:
a. The area of the polyhedron is gotten by finding the area of each individual shape.
The area of the left rectangle with sides 6 by 4 is 6 cm × 4 cm = 24 cm²
The area of the middle rectangle with sides 6 by 5 is 6 cm × 5 cm = 30 cm²
The area of the right rectangle with sides 6 by 3 is 6 cm × 3 cm = 18 cm²
The area of the triangle on the left rectangle is found using heron's formula where area A = √[s(s -a)(s -b)(s -c) where s = (a + b + c)/2 and a, b and c are the sides of the rectangle.
Since the rectangle has sides 4, 3 and 5, a = 4, b = 3 and c = 5
So, s = (a + b + c)/2 = s = (4 + 3 + 5)/2 = 12/2 = 6
A = √[s(s -a)(s -b)(s -c)
= √[6(6 - 4)(6 - 3)(6 - 5)
= √[6(2)(3)(1)
= √36
= 6 cm²
The area of the triangle on the right rectangle is found using heron's formula where area A = √[s(s -a)(s -b)(s -c) where s = (a + b + c)/2 and a, b and c are the sides of the rectangle.
Since the rectangle has sides 3, 4 and 5, a = 3, b = 4 and c = 5
So, s = (a + b + c)/2 = s = (3 + 4 + 5)/2 = 12/2 = 6
A = √[s(s -a)(s -b)(s -c)]
= √[6(6 - 3)(6 - 4)(6 - 5)]
= √[6(3)(2)(1)
= √36
= 6 cm²
The surface area of the polyhedron is the sum of all the areas. So, A = 24 cm² + 30 cm² + 18 cm² + 6 cm² + 6 cm² = 84 cm²
b. Explain your reasoning
The area of the polyhedron is found by finding the sum of the areas of each individual shape.
