This trapezoid is made up of two right triangles and one rectangle.

Mathematics

1 answer:

artcher [175]2 years ago

5 0

9514 1404 393

Answer:

each triangle: 29.75 in²
rectangle: 374 in²
total area: 433.5 in²

Step-by-step explanation:

The base of each triangle is half the difference between the bases of the trapezoid:

(29 in -22 in)/2 = 7 in/2 = 3.5 in

The area of the triangle is given by the formula ...

A = 1/2bh

A = 1/2(3.5 in)(17 in) = 29.75 in² . . . triangle area

The area of the central rectangle is the product of its base and height.

A = bh = (22 in)(17 in) = 374 in² . . . rectangle area

The total area of the trapezoid is the sum of the areas of the two triangles and the area of the rectangle.

total area = 2(29.75 in²) + 374 in² = 433.5 in² . . . total trapezoid area

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Arte-miy333 [17]

Answer:

400 square meters

Step-by-step explanation:

We can first solve this problem with each unit representing 1 centimeter, and then scale up at the very end. The shape that we have a parallelogram. The base is 8 cm, and the height is 2 cm. The formula for the area of a parallelogram is just $bh$ , so the area of the parallelogram is 16 square centimeters. However, now we scale up. Since each centimeter correlates to 5 meters, each little box will correlate to 25 square meters. Therefore, $16 \cdot 25 = \boxed{400}$ square meters is our answer

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2 years ago

find the point-slope equation of the line perpendicular to the line y=2x+5 passing through the point (1,4). (please include solu

pishuonlain [190]

First off, let's keep in mind that perpendicular lines have negative reciprocal slopes, hmmm so what's the slope of y = 2x + 5?

well, notice, that equation is in slope-intercept form, thus $\bf y=\stackrel{slope}{2}x+5$ .

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}}
{2\implies \stackrel{slope}{\cfrac{2}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{2}}\qquad \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}$

so, we're really looking for the equation of a line whose slope is -1/2 and runs through 1,4.

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad \qquad \qquad 
slope = m\implies -\cfrac{1}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=-\cfrac{1}{2}(x-1)$

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2 years ago

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emmasim [6.3K]

Answer:

The radius of the circle r=12.

The area of a circle is 144π.

Step-by-step explanation:

The radius of the circle is r where 2πr=24π, r=12.

The area of a circle with radius 12 is

A=πr², A=π12², A=144π.

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