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Mathematics

2 answers:

WINSTONCH [101]2 years ago

8 0

Answer: 170

Step-by-step explanation: Like I answered before: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.

Gekata [30.6K]2 years ago

8 0

Answer:

<CDA = 170⁰

Step-by-step explanation:

<A + <D = 180⁰ { Adjacent Angles of an parallelogram are supplementary}

10⁰ + <D = 180⁰

<D = 180⁰ - 10⁰ = 170⁰

<D = x⁰ = 170⁰ = <CDA

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1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythegorean theorem, as shown in the picture, the height is $\frac{ \sqrt{3} }{2} a$

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one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is $2*( \frac{1}{2} *a* \frac{ \sqrt{3} }{2}a )=\frac{ \sqrt{3} }{2} a^{2}$

so the total area of the roof is $\frac{ \sqrt{3} }{2} a^{2} +3al$

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
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5. so the area now is $\frac{ \sqrt{3} }{2} a^{2} +2al$

6. now a=25 and l=2a=50

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=3041.3 (ft squared)