A company can manufacture x hundred items for a total cost of C=300+1200x-100x. Find x if the total cost is 3,000

How would you go about finding the area and perimeter of a composite figure?

fgiga [73]

Explanation:

The area is the sum of the areas of the non-overlapping parts. The figure is called "composite" because it is composed of figures whose area formulas you know. Decompose the figure into those, find the area of each, then sum those areas to find the area of the whole.

<u>For example</u>

If the figure consists of a rectangle and semicircle, find the areas of each of those. Then add the areas together to find the total area.

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Likewise, the perimeter of a composite figure will be the sum of the "exposed" perimeters of the parts. (Some edges of the figures making up the composition will be internal, so do not count toward the perimeter of the composite figure.)

<u>For example</u>

If the curved edge of the semicircle of the figure described in the example above is part of the perimeter, then its length will be half the circumference of a circle. If the straight edge of the semicircle is "internal" and not a part of the perimeter, its length (the diameter of the semicircle) may need to be partially or wholly subtracted from the perimeter of the rectangle, depending on the actual arrangement of the composite figure. In other words, add up the lengths of the edges that "show."

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<em>Additional comments</em>

In the above, we have described how to add the areas of parts of the figure. In some cases, it can be easier to identify a larger figure, or one that is more "complete", then subtract the areas of the parts that aren't there. For example, an L-shaped figure can be decomposed into two rectangles. Or it can be decomposed into a larger rectangle covering the entire outside dimensions, from which a smaller rectangle is subtracted to leave the L-shape. Depending on how dimensions are shown, one computation or the other may be easier.

Likewise, for the purposes of computing the perimeter, lines of the figure may be rearranged in any convenient way, as long as their total length doesn't change. The L-shape just described will have a perimeter exactly equal to the perimeter of the rectangle that encloses its outside dimensions, for example. You can see this if you move the two lines forming the concave edges.

Familiarity with area formulas can help with area. For example, you know that the area of a triangle is the same as that of a rectangle half the height. Likewise, the area of a trapezoid is the area of a rectangle with the same height and a width equal to the midline of the trapezoid.

5 0

3 years ago

A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti

yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have $b=\frac{42}{h}$ . Then, you can replace it in equation 1.