Find the distance between the points (4,5) and (10, – 3). Round decimals to the nearest tenth
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Answer:
<h3>Option D) 294 sq cm is correct</h3><h3>∴ the surface area of the rectangular pyramid is 294 sq cm</h3>Step-by-step explanation:
First we have to split the net into 4 triangles and 1 rectangle
Given a = 12 cm ,b = 6 cm and d = 13 cm
<h3>To find the surface area of the rectangular pyramid:</h3>Now find the area of the rectangle base
= 72 sq. cm
<h3>∴ Rectangle base area=72 sq cm</h3>Now to find the area of the triangle on the left
= 39 sq cm
<h3>∴ Left triangle=39 sq cm</h3>Since all the triangles are congruent , you will need to multiply by 2 to get the combined area of the triangle on the left and on the right.
Area of left and right triangles= 2(39)
=78 sq cm
<h3>∴ Area of left and right triangles=78 sq cm</h3>Find the area of the triangle on the bottom
= 72 sq cm
<h3>∴ Bottom triangle area=72 sq cm</h3>Since the bottom of the triangle is congruent to the top triangle, multiply that by 2 to get a combined area of the triangle on the bottom and top
Area of top & bottom triangles=2 (72)
= 144 sq cm
<h3>∴ Area of top & bottom triangles= 144 sq cm</h3>Finally add the area of the 4 triangles to the area of the rectangular base we get
=72 + 78 + 144
= 294 sq cm
<h3>∴ the surface area of the rectangular pyramid is 294 sq cm</h3><h3>∴ option D) 294 sq cm is correct.</h3>
Check the picture below.
so, to get the area of the triangles, we can simply run a perpendicular line from the top to the base, and end up with a right-triangle with a base of 22 and a hypotenuse of 34, let's find the altitude.
so then the surface area of the triangular prism is,
![\bf \stackrel{\textit{left and right}}{2(34\cdot 76)}~~+~~\stackrel{\textit{bottom}}{(44\cdot 76)}~~+~~\stackrel{\textit{front and back}}{2\left[\cfrac{1}{2}(44)(\sqrt{672}) \right]} \\\\\\ 8512~~+~~(44)(\sqrt{672})\qquad \approx\qquad 9652.61036291978](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bleft%20and%20right%7D%7D%7B2%2834%5Ccdot%2076%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Bbottom%7D%7D%7B%2844%5Ccdot%2076%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Bfront%20and%20back%7D%7D%7B2%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%2844%29%28%5Csqrt%7B672%7D%29%20%20%5Cright%5D%7D%0A%5C%5C%5C%5C%5C%5C%0A8512~~%2B~~%2844%29%28%5Csqrt%7B672%7D%29%5Cqquad%20%5Capprox%5Cqquad%209652.61036291978)
so, to get the area of the triangles, we can simply run a perpendicular line from the top to the base, and end up with a right-triangle with a base of 22 and a hypotenuse of 34, let's find the altitude.
so then the surface area of the triangular prism is,