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2 years ago

(image) The figure below is an isosceles triangle surmounted by a semi-circle. Find the area of the entire region.

Mathematics

1 answer:

S_A_V [24]2 years ago

5 0

Answer:

12.53

Step-by-step explanation:

∠BCA = (180°-40°)/2 = 70°

Laws of Sines: CA/sin 40° = AB/sin 70° = 5/sin 70°

CA = 5/sin 70° * sin 40° = 3.40

area of semicircle CA = (3.1416 * 1.70²) / 2 = 4.54

By Heron's Formula, area of triangle ABC:

1/4 √(a+b+c) (a+b-c) (b+c-a) (c+a-b) = 1/4 * √13.4*3.4*3.4*6.6

= 7.99

Entire region area = 4.54 + 7.99 = 12.53

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Step-by-step explanation:

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3 years ago

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3 years ago

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3 years ago

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$\fbox{Solution by using Matrix}$

$\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20$

$\text{Rewrite the linear equations above as a matrix}$

$\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right]$

$\text{Apply to Row2 : Row2 + Row1}$

$\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right]$

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$\text{ Simplify rows}$

$\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right]$

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$x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}$

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3 years ago