Here is a triangular prism. 4 cm 10 cm 5cm 5cm 6cm
1 answer:
Answer:
(A) 120 cm³
(B) 184 cm²
Step-by-step explanation:
(A)
Assuming the diagram attached is thesame as the one needed to complete the question,
Applying
V = A'×L................... Equation 1
Where V = volume of the prism, A' = Area of the triangular base, L = Length of the prism.
But,
A' = 1/2bh............. Equation 2
Where b = base of the triangle, h = height of the triangle.
Substitute equation 2 into equation 1
V = 1/2bh(L)............... Equation 3
From the question,
Given: b = 6 cm, h = 4 cm, L = 10 cm
Substitute these values into equation 3
V = 1/2(6×4×10)
V = 120 cm³
(B)
Surface area of the prism(A) = bh+L(a+b+c).............. Equation 4
Given: b = 6 cm, b = 5 cm, c = 5 cm, L = 10 cm, h = 4 cm
Substitute these values into equation 4
A = (6×4)+10(5+5+6)
A = 24+160
A = 184 cm²
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We know, the sum of the acute angles in a right triangle is 90°.
Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90
Substitute (1) to (2):
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Substitute the value of x to (3)
Answer: x = 3 and y = 1.
