Mathematics, 28.07.2019 03:00 bermudezs732

Figure abcde has vertices a(−2, 3), b(2, 3), c(5, −2), d(0, −4), and e(−2, −2). plot the points on your own coordinate grid and connect the points in alphabetical order. decompose figure abcde into rectangles and triangles. part a: how many triangles and rectangles did you make? (1 point) part b: use figure abcde created on your coordinate grid to find the lengths, in units, of sides ab and ae. (4 points) part c: what is the area of figure abcde? show your work. (5 points

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Answer from: Angelofpink2590

Part A: Figure ABCDE is drawn (see added picture). There are one rectangle ABFE and two triangles BFC and ECD.

Part B: The distance from point A to the y-axis is 2 units and the distance from point B to y-axis is 2 units, then AB=4 units. Similarly, the distance from point A to x-axis is 3 units and the distance from point E to x-axis is 2 units, then AE=5 units.

Part C: From the part A figure ABCDE consists of rectangle ABFE and triangles BFC and EDC. The area of figure ABCDE isthe sum of all three area.

$A_{ABFE}=AB\cdot AE=4\cdot 5=20$ sq. un.

$A_{BFC}=\dfrac{1}{2}BF\cdot FC= \dfrac{1}{2}5\cdot 3=7.5$ sq. un.

$A_{EDC}=\dfrac{1}{2} EC\cdot DP=\dfrac{1}{2} 7\cdot 2=7$ sq. un.,

then

$A_{ABCDE}=20+7.5+7=34.5$ sq.un.

Figure abcde has vertices a(−2, 3), b(2, 3), c(5, −2), d(0, −4), and e(−2, −2). plot the points on y

Answer from: BardiFan

The correct answers are:

Part A: I used 1 rectangle and 2 triangles (figure attached).

Part B: AE = 5 units and AB = 4 units.

Part C: The area is 34.5 square units.

Explanation:

Part A: The drawing is attached.

Part B: Counting across from A to B, we see it is a straight horizontal line segment. It goes from -2 to 2; this is a difference of (2--2) = 2+2 = 4 units.

Counting down from A to E, we see it is a straight vertical line segment. It goes from 3 to -2; this is a difference of (3--2) = 3+2 = 5 units.

Part C: To find the area of ABCDE, we find the area of the rectangle and two triangles I've drawn.

The rectangle has dimensions 5 by 4; the area would then be 5(4) = 20 square units.

The area of the triangle to the right of the rectangle is given by the formula A = 1/2bh. In this triangle, the base is 3 units and the height is 5 units; the area is then A = 1/2(3)(5) = 1/2(15) = 7.5 square units.

The area of the triangle below the rectangle is given by the formula A = 1/2bh. In this triangle, the base is 7 units and the height is 2 units; this makes the area A = 1/2(7)(2) = 1/2(14) = 7 square units.

The total area is then 20+7.5+7 = 34.5 square units.