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Anna35 [415]
3 years ago
14

(05.03)Bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate th

e area of the polygon. Be sure to show all your work and explain your answer.
+17 pts BRAINLIEST ONLY IF FAST

Mathematics
1 answer:
Amanda [17]3 years ago
7 0
Given : Bev has to cut her grandma's grass this weekend
Six-sided polygon that includes two isosceles right triangles, one with height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet.
To Find : Area of Polygon
Solution:
Area of triangle = (1/2) bh
= (1/2) * 15 * 15
= 112.5 sq feet
= (1/2) * 4 * 4
= 8 sq feet
Area of rectangle = 25 x 4 = 100 sq feet
Total area =112.5 + 8 + 100
= 220.5 sq feet
Area of Polygon = 220.5 sq feet
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A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
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Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

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Angle sum property,

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\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

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∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

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