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dlinn [17]
3 years ago
12

Math homework please help look at picture!!

Mathematics
1 answer:
melisa1 [442]3 years ago
5 0

Answer:

a = 327 m²

Step-by-step explanation:

Area of bed

r = 22/2 = 11

a = 3.14(11²)

a = 379.94

Area of bed and sidewalk

r = 11 + 4 = 15

a = 3.14(15²)

a = 706.5

Area of sidewalk

a = 706.5 - 379.94

a = 327 m² (rounded to whole number

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\bigstar  (Hypotenuse)² = (First Leg)² + (Second leg)²

In Triangle, ADB : AB is the Hypotenuse, AD is the First leg and BD is the Second leg

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Substituting the values, We get :

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:\implies  (AD)² = 225 - 81

:\implies  (AD)² = 144

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:\implies  AD = 12

We know that, In a Right angled Triangle :

\bigstar\;\;\boxed{\mathsf{Tan\theta = \dfrac{Opposite\;Side}{Adjacent\;Side}}}

Now, Consider Triangle ADC : With respect to 45° Angle, AD is the Opposite Side and DC is the Adjacent Side

:\implies \mathsf{In\;Triangle\;ADC,\;Tan45^{\circ} = \dfrac{AD}{DC}}

\mathsf{:\implies 1 = \dfrac{12}{DC}}

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:\implies  Total Length of the Base (BC) = BD + DC

:\implies  Total Length of the Base (BC) = 9 + 12

:\implies Total Length of the Base (BC) = 21

We know that, Area of the Triangle is given by :

\bigstar\;\;\boxed{\mathsf{Area = \dfrac{1}{2} \times Base \times Height}}

In Triangle, ABC : AD is the Height and BC is the Base

:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times BC \times AD}

:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times 21 \times 12}

:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = (21 \times 6)}

:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = 126}

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Step-by-step explanation:

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