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3 years ago

What is the area of the figure? Enter your answer in the box.

Mathematics

1 answer:

nordsb [41]3 years ago

6 0

Answer:

The area of the figure = 112 in²

Step-by-step explanation:

The figure consist of:

1) A square of side length of 10 in.

2) A right triangle with a base of (10 - 6 = 4 in) and a height of (16 - 10 = 6 in)

So,

The area of the square = (side length)² = 10² = 100 in²

The area of the triangle = 0.5 * height * base = 0.5 * 6 * 4 = 12 in²

So,

The total area = 100 + 12 = 112 in²

<u>The area of the figure = 112 in²</u>

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Step-by-step explanation:

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

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The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

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The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

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3 years ago

What is the x-coordinate of the vertex of the parabola whose equation is y = 3x2 + 9x?

inn [45]

Hello :
y = 3x²+9x
= 3(x² + 3x )
= 3 ( x² +2(3/2)x +(3/2)²) -(3/2)²)
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y = 3 (x+3/2)² -27/4
<span>the x-coordinate of the vertex is : - 3/2</span>

8 0

3 years ago

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