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Transcript: Here is a 'sketch' of what the chateau should look like in the end. 2 Overlap: Overlapping Pt. 2 2 Surface Area of Rectangle The side lengths of the square shall be length: 10 meters width: 8 meters and height: 4 meters. Pokemon PowerPoint Now to calculate the over lap. We must subtract the total surface area which is 385 m2 with the base and length which is 105m2. So 385-105=280 Remember that the formula for the Surface Area of the Rectangular/Square Prism is SA= 2( lw + wh + lh) 385-105=280m2 As you can see here, there are four equal bars on top of the rectangular base we just did. So we must calculate one bar, multiply it by four and then subtract it from the surface area of the rectangle. According to my blueprint, the dimensions are length 4m, width 2m height 4cm. SA = bh + 2ls + lb SA = 8 x 2.5 + 2(10 x 2.5) + 10 x 8 SA = 20 + 2 x 25 + 80 SA = 20 + 50 + 80 SA = 150 m Rectangle Total Surface Area Overlap: Next we need to find the surface area of the square. Step 1 Cont. Overlap: Circles! First, we must figure out the surface area of the base. The base has 2 shapes: a rectangle and a square. 8 sides: 1 back, 4 sides, 3 front. Triangular prism Now we must add another roof for the doorway. Side Lengths are length - 10 base =8 height = 2.5 Now its time to calculate the surface area we just added to the chateau to give it a pokemon feel to it. The formula for the surface area of a circle which is simply: 2 Just joking. But seriously Its 2πr And the diameter is about 26cm Overlap Part 1 Overlap: Now we must put in the substitutions. (Remember Length x Width is the face that is overlapping and Height x Length is the sides.) SA= 4[(lw) + 2(hl)] SA = 4[(4x2) + 2(0.04 x 4)] SA = 4[(8) + 2(0.16)] SA = 4[8 + (0.32)] SA = 4[8.32] SA = 33.28 The surface area is 756m Next we do the roof, which in this case is a triangular prism. The formula for a triangular prism SA= bh/2 + 2ls + lb Lets say the dimensions are b=14, h= 5, l=21, s=5 Now since the square we just calculated has 3 sides that are covered, we must subtract those sides from the total surface area. The sides that are covered are the top, bottom and back. Now we just use our previous work to help us to find the answer. The formula we are going to use is: SA - (lw + wh + lh) 304 - (10 x 8 + 8 x 4 + 10 x 4) 304 - (80 + 32 + 40) 304 - (152) = 152 SA = 2 (lw + wh + lh) SA = 2 (10 x 8 + 8 x 4 + 10 x 4) Step 3.3 Bars Triangles The side lengths of the rectangle shall be about length = 14 meters, width = 21 meters, height = 4 meters Step 1.9 Overlap Pt3 SA = 2 ( 80 + 32 + 40) SA = 2 x 152 SA = 304 This world is full of shapes and sizes. Today I need your help to a build a chateau in Sinnoh Firstly, we are going to calculate the two triangles in the front and the back. The formula to calculate them is: SA=bh/2 but since there is two equal triangles its bh/2 x 2, which leaves us with SA=bh for the two triangles To calculate the surface area of this shape, the formula is (length x width). The sides of the bars are (Height x length) but that is not calculated into the overlap because it is not overlapping anything. To put it in a formula, it is SA= (lw)+(hl) STEP 1 In order to build a chateau, we will need to find the right amount of wood for the walls and such. So to calculate the recent surface area we must get the total area and subtract it by the side that is doing the overlap, which is the base of the square. So, the equation is 150-80, which equals 70. SA= bh + 2ls + lb SA= 14x5 + 2(21x5) + 21x5 SA= 70 + 2(105) + 105 SA= 70 + 210 + 105 SA= 385m2 So the surface area of the roof is 385 m2 SA= 2( lw + wh + lh) SA= 2( 14x21 + 21x4 + 14x4) SA= 2( 294 + 84 + 56) SA= 2(434) SA= 868 The Surface Area is 868m 150-80=70 2 Hello there! My name is Rowan. But most people call me the Pokemon Professor. 2 . The Part that is overlapping is a different story Its simply the LW x 4. SA= 4(4x2) SA = 4(8) SA= 32m 2 Finally, we must figure out how much wood we need to build the chateau with by adding all the surface areas we calculated together (overlaps included). Surface Area of the Surface area of Surface area Small Surface square with the circle of the roof Roof area of the overlap rectangle 152 + 175.3 + 280 + 70 + 756 So in conclusion, we must have about 1434m of wood to build this chateau. Step 1 Cont cont cont cont. Step 1 CONT cont. cont... Now we must overlap the existing surface areas of the rectangle and the square. To do that, we must subtract the side of the square that is overlapping the rectangle, and subtract that from the rectangle. Also, we must subtract the bars on top of the rectangles to find the remainder overlap. 868 - 80 - 32 = 756 Circles Pt. 2 :D 2 We must put the substitution. SA = 2π x 13 SA = 2π x 169 SA = 175.2831853071796... SA = 175.3 Surface Area of Square: r So the surface area is 304m Step 2.9 Overlap 2 Now to add the substitutions: 2 Square
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