Sketch the following to help answer the question. Kite WXYZ has a short diagonal of XZ and a long diagonal of WY. The diagonals
intersect at point V. The length of XZ = 8cm, the length of segment WV is 6√3, and the ∠XYV = 30°. Find the exact area of kite WXYZ.
2 answers:
Answer: 69.281cm2
Step-by-step explanation: first we sketch the kite, which I have done is the picture attached
To find the area, we divide the kite into two triangles, cutting the kite at the line XZ
So we have two triangles, XWZ and XYZ
We know that finding the area of a triangle is half of it's base multiplied by the height
A = 1/2bh
For triangle XWZ we have a base of 8cm and a height of 6root3cm
Finding the area
1/2 x 8 x 6root3 = 41.569cm2
For triangle XYZ we have the base, but we don't have the height
So to get the height we use tan rule
We states that tan of an acute angle in a right angle triangle equals to the value of the length opposite the angle divided by the value of the length adjacent to it, popular known as "TOA"
Since XY and XZ are the same lengths (properties of a kite)
We can tell that XV is half of XZ
So XV = 8/2 = 4cm
We label the height we are looking for as x
So therefore
Tan30 = 4/x
xtan30 = 4
x = 4/tan30 = 6.928
So therefore
Area of triangle XYZ
1/2 x 8 x 6.928 = 27.712cm2
Adding the two Areas together = 41.569+27.712 = 69.28cm2
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Step-by-step explanation:
This is a <u>system of equations</u>.
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We simplify and solve for <em>y</em>:
→
→
→
Now, we plug in the value for <em>y</em>, which is 3, into either equation. I will just use the first equation:
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Let me know if my explanation is unclear.
Answer:
Step-by-step explanation:
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2
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=
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The complete question is
<span>Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog house are a = 2 feet, b = 1 foot, and c = 1.4 feet.
</span><span>If Bradley plans to paint the outside of the dog house blue, not including the bottom, how many square feet of paint will he use?
the picture in the attached figure
</span>
we know that
surface area of the figure=surface area of cube+surface area of triangular prism
surface area of cube=4*a²----> 4*2²-----> 16 ft²
surface area of triangular prism=2*[a*c]+2*[a*b/2]---> 2*[2*1.4]+[2*1]
surface area of triangular prism=5.6+2----> 7.6 ft²
surface area of the figure=16 ft²+7.6 ft²----> 23.6 ft²
the answer is
23.6 ft²
<span>Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog house are a = 2 feet, b = 1 foot, and c = 1.4 feet.
</span><span>If Bradley plans to paint the outside of the dog house blue, not including the bottom, how many square feet of paint will he use?
the picture in the attached figure
</span>
we know that
surface area of the figure=surface area of cube+surface area of triangular prism
surface area of cube=4*a²----> 4*2²-----> 16 ft²
surface area of triangular prism=2*[a*c]+2*[a*b/2]---> 2*[2*1.4]+[2*1]
surface area of triangular prism=5.6+2----> 7.6 ft²
surface area of the figure=16 ft²+7.6 ft²----> 23.6 ft²
the answer is
23.6 ft²