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Answer:
The total surface area of the prism is 620 cm²
Step-by-step explanation:
The total area of the prism = lateral area + 2 (area of the cross-section)
The lateral area = perimeter of the cross-section × height
∵ The cross-section of the prism is an isosceles triangle
∵ The sides of the triangle are 13 cm, 13 cm, 24 cm
∵ The perimeter of the triangle is the sum of its sides
∴ The perimeter = 13 + 13 + 24 = 50 cm
∴ The perimeter of the cross-section = 50 cm
∵ The height of the prism is 10 cm
→ Use the rule of the lateral area above to find it
∴ The lateral area of the prism = 50 × 10 = 500 cm²
∵ The area of the triangle = × base × height
∵ The base of the triangle = 24 cm
∵ The height of the triangle = 5 cm
∴ The area of the triangle = × 24 × 5 = 60 cm²
∴ The area of the cross-section = 60 cm²
→ Substitute the lateral area and the area of the cross-section in the rule
of the total surface area above
∵ The surface area = 500 + 2(60)
∴ The surface area = 500 + 120
∴ The surface area = 620 cm²
∴ The total surface area of the prism is 620 cm²
The <em>missing</em> end of the <em>line</em> segment whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).
<h3>How to locate the missing end of a line segment</h3>
In this question we know an end and a midpoint of a <em>line</em> segment. The <em>missing</em> end can be found from the following formula:
M(x, y) = G(x, y) + 0.5 · [H(x, y) - G(x, y)]
M(x, y) = 0.5 · G(x, y) + 0.5 · H(x, y)
0.5 · H(x, y) = M(x, y) - 0.5 · G(x, y)
H(x, y) = 2 · M(x, y) - G(x, y) (1)
If we know that M(x, y) = (5, 3) and G(x, y) = (1, -5), then the coordinates of the point H are:
H(x, y) = 2 · (5, 3) - (1, -5)
H(x, y) = (10, 6) - (1, -5)
H(x, y) = (9, 11)
The <em>missing</em> end of the <em>line</em> segment whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).
To learn more on line segments: brainly.com/question/25727583
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The simplest way to do this is to use the formula where
is equal to slope.
(2--6)/(4--2)= 8/6.
Hope this helps!
is equal to slope.
(2--6)/(4--2)= 8/6.
Hope this helps!