What is the area of the polygon?
2 answers:
Hey there!
Let's split this up into four parts as shown by the image here.
Focus on the section to the far left. It is 2 units wide and 5 units long.
The formula for the area of a triangle is A = 1/2 x l x w.
A = 1/2 x 5 x 2 = 2.5 x 2 = 5 square units is the area of this section.
The second section, the rectangular one, has the dimensions 3 x 5.
The area of this section is 15 square units.
The third section is the one at the top left. It is 4 units wide and 2 units long.
A = 1/2 x 2 x 4 = 1 x 4 = 4 square units is the area of this section.
The last section is the one at the bottom right. It is 4 units wide and 3 units long.
A = 1/2 x 3 x 4 = 1.5 x 4 = 6 square units is the area of this section.
Now to find the total area of the polygon, which happens to be an irregular pentagon, add up the areas of the sections we divided earlier.
5 + 15 + 4 + 6 = 30
The area of this polygon is 30 square units, or 30 u².
Hope this helps!
Let's split this up into four parts as shown by the image here.
Focus on the section to the far left. It is 2 units wide and 5 units long.
The formula for the area of a triangle is A = 1/2 x l x w.
A = 1/2 x 5 x 2 = 2.5 x 2 = 5 square units is the area of this section.
The second section, the rectangular one, has the dimensions 3 x 5.
The area of this section is 15 square units.
The third section is the one at the top left. It is 4 units wide and 2 units long.
A = 1/2 x 2 x 4 = 1 x 4 = 4 square units is the area of this section.
The last section is the one at the bottom right. It is 4 units wide and 3 units long.
A = 1/2 x 3 x 4 = 1.5 x 4 = 6 square units is the area of this section.
Now to find the total area of the polygon, which happens to be an irregular pentagon, add up the areas of the sections we divided earlier.
5 + 15 + 4 + 6 = 30
The area of this polygon is 30 square units, or 30 u².
Hope this helps!
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For D, it's like C, but you dont have the chart. Use subtraction to find the slope. Change in y over change in x (which means subtract the y values and divide them by the difference in x values). So. You'd do 0 - 3 over -6 - 3 which equals -3 over -9, which simplifies to 1/3. And that's your slope! So to find the y-int just do the same thing you did in the last problem, plug in an ordered pair and the slope into the slope-intercept equation and solve as a one step equation (steps in picture). And there you have it, the slope which is 1/3, and the y-int which is 2.
For B, the same thing. Converting to slope-intercept form, just with an extra step. First, you would subtract 1y from both sides to move it to the left of the equal sign, since that's where it needs to be for slope-intercept form. That gives you -1y + 7 = -x. Don't worry about the negatives for now. Next, subtract 7 from both sides to get y by itself on the left (because that's how it is in slope-intercept form) which gives you -1y = -x - 7. Then, because you can't have negative variables, divide both sides by negative 1 (a negative divided by a negative equals a positive), to equal y = x + 7. (I've attached a picture showing my steps if the words are too confusing)
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