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HELP ME FOR 50 POINTS PLSSS​

HELP ME FOR 50 POINTS PLSSS​-example-1
User Arrowcatch
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1 Answer

5 votes

Answer:

13. 7.5 square units

14. 24.5 square units

Explanation:

Question 13

Given vertices:

  • E = (3, 1)
  • F = (3, -2)
  • G = (-2, -2)

As points E and F share the same x-value and points F and G share the same y-value, the polygon is a right triangle with base GF and height FE.

As points F and G share the same y-value, the length of line segment GF is the difference between the x-values:


\begin{aligned} \implies \overline{GF}&=x_F-x_G\\&=3-(-2)\\&=3+2\\&=5\end{aligned}

As points E and F share the same x-value, the length of line segment FE is the difference between the y-values:


\begin{aligned} \implies \overline{FE}&=y_E-x_F\\&=1-(-2)\\&=1+2\\&=3\end{aligned}

Therefore, the area of polygon EFG is:


\begin{aligned}\textsf{Area of a triangle}&=(1)/(2) * \sf base * height\\\\\implies \textsf{Area of polygon $EFG$}&=(1)/(2) * \overline{GF} * \overline{FE}\\\\&=(1)/(2) * 5 * 3\\\\&=(15)/(2)\\\\&=7.5\;\; \sf units^2\end{aligned}

Question 14

Given vertices:

  • J = (-3, 4)
  • K = (4, 4)
  • L = (3, -3)

As points J and K share the same y-value the polygon is a triangle with base JK and height of the difference in y-values of points K and L.

As points J and K share the same y-value, the length of line segment JK is the difference between the x-values:


\begin{aligned} \implies \overline{JK}&=x_K-x_J\\&=4-(-3)\\&=4+3\\&=7\end{aligned}

The height of the triangle is the difference between the y-values of points K and L:


\begin{aligned} \implies\sf Height&=y_K-y_L\\&=4-(-3)\\&=4+3\\&=7\end{aligned}

Therefore, the area of polygon JKL is:


\begin{aligned}\textsf{Area of a triangle}&=(1)/(2) * \sf base * height\\\\\implies \textsf{Area of polygon $JKL$}&=(1)/(2) * \overline{JK} * \sf height \\\\&=(1)/(2) * 7 *7\\\\&=(49)/(2)\\\\&=24.5\;\; \sf units^2\end{aligned}

HELP ME FOR 50 POINTS PLSSS​-example-1
HELP ME FOR 50 POINTS PLSSS​-example-2
User Rarrarrarrr
by
3.3k points