A hotel is designing a new lobby. The lobby shape is a rectangle with two congruent right triangles on either side, as shown bel
ow.
What is the total area, in square feet, of the lobby?
What is the total area, in square feet, of the lobby?
2 answers:
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Area of a regular polygon = 1/2 x apothem x perimeter
We know that each side is 10, because if you draw a segment from the center to a vertex it creates a 30-60-90 triangle (those are the angles). This type of triangle has a ratio for its sides where the longer side is radical three times as long as the shorter leg. This shorter leg happens to be half of a side of the polygon. Knowing that the polygon has 6 sides, we can multiply 10 by 6 to get the perimeter.
Area of polygon = 1/2 x apothem x perimeter = 1/2 x 5
x 60
=30 x 5
= 30 x 5 x <span>1.73205080757
= 150 x </span><span>1.73205080757
= </span><span>259.807621135
To the nearest tenth of a cm, the area of the polygon is 260 cm squared</span>
We know that each side is 10, because if you draw a segment from the center to a vertex it creates a 30-60-90 triangle (those are the angles). This type of triangle has a ratio for its sides where the longer side is radical three times as long as the shorter leg. This shorter leg happens to be half of a side of the polygon. Knowing that the polygon has 6 sides, we can multiply 10 by 6 to get the perimeter.
Area of polygon = 1/2 x apothem x perimeter = 1/2 x 5
=30 x 5
= 30 x 5 x <span>1.73205080757
= 150 x </span><span>1.73205080757
= </span><span>259.807621135
To the nearest tenth of a cm, the area of the polygon is 260 cm squared</span>
Não, não podemos fazer um triângulo com os comprimentos dos lados de 2 cm, 3 cm e 10 cm. Isso ocorre porque a soma de 2+3 < 10. (in english: No, we cannot make a triangle with the side lengths of measurement 2 cm, 3 cm, and 10 cm. This is because sum of 2+3 < 10).
<h3>What is triangle inequality theorem?</h3>Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
Now, for this case, the sides given are:
- a =2 cm,
- b = 3 cm,
- and c = 10 cm
But we see that:
a+ b = 5 cm which is < c which is of 10 cm.
Thus, these lengths don't satisfy the triangle inequality theorem, and therefore, cannot be sides of any triangle.
Learn more about triangle inequality theorem here:
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