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3 years ago

I NEED HELP ASAP Find the area of the trapezoid by decomposing it into other shapes.

Mathematics

1 answer:

disa [49]3 years ago

7 0

Answer:

Area of the trapezoid is 38 cm²

Step-by-step explanation:

Step 1: Area of the trapezoid can be found by decomposing it into 2 triangles and a rectangle.

Step 2: Find area of first triangle. Given base = 5 cm and height = 4 cm

Substitute in formula for area of triangle = 1/2 base * height

Area of triangle, A1 = 1/2 * 5 * 4 = 10 cm²

Step 3: Find area of rectangle. Given breadth = 4 cm (Same as height of triangles) Length = 6 cm. Substitute in formula for area of rectangle = length * breadth

Area of rectangle, A2 = 4 * 6 = 24 cm²

Step 4: Find area of second triangle. Given height = 4 cm (same as the other triangle) and base = 2 cm (8 cm - 6 cm)

Substitute in formula for area of triangle = 1/2 base * height

Area of triangle, A3 = 1/2 * 2 * 4 = 4 cm²

Step 5: Calculate total area = A1 + A2 + A3 = 10 + 24 + 4 = 38 cm²

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3 years ago

The given line passes through the points and (-4, -3) and (4, 1).

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Answer:

The equation of the line is y - 3 = -2(x + 4)

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line which passes through the points (x1 , y1) and

(x2 , y2) is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The product of the slopes of the perpendicular lines = -1

- That means if the slope of a line is m then the slope of the

perpendicular line to this line is -1/m

- The point-slope of the equation is $y - y_{1}=m(x - x_{1})$

* lets solve the problem

∵ A given line passes through points (-4 , -3) and (4 , 1)

∴ x1 = -4 , x2 = 4 and y1 = -3 , y2 = 1

∴ The slope of the line $m=\frac{1-(-3)}{4-(-4)}=\frac{1+3}{4+4}=\frac{4}{8}=\frac{1}{2}$

- The slope of the line perpendicular to this line is -1/m

∵ m = 1/2

∴ The slope of the perpendicular line is -2

- Lets find the equation of the line whose slope is -2 and passes

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∵ x1 = -4 , y1 = 3

∵ m = -2

∵ y - y1 = m(x - x1)

∴ y - 3 = -2(x - (-4))

∴ y - 3 = -2(x + 4)

* The equation of the line is y - 3 = -2(x + 4)

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3 years ago

It is known that 50% of adult workers have a high school diploma. If a random sample of 8 adult workers is selected, what is the

son4ous [18]

Answer:

85.56% probability that less than 6 of them have a high school diploma

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have a high school diploma, or they do not. The probability of an adult having a high school diploma is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$