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3 years ago

Geometry help?? 11-13

Mathematics

1 answer:

aalyn [17]3 years ago

7 0

I'm guessing these are regular polygons so... here goes.... 11. angle 1 is (8-2)*180= 1080 then divide that by 8 (how many angles there are ) to get 135. angle 2 is 360/8 (the sum of the exterior angle is always 360) which is 45 and multiply it by 2 (because the two polygons are stuck together) to get 90.
12. it says 2 squares so angle 4 is definitely 90. angles 3 and 5 would be 45 because it's an isosceles right triangle meaning that 1 angle is 90 and that the total of the other two angles would be 90 as a triangle angle sum is 180 and since it's isosceles just divide 90 by 2 because the 2 angles are the same getting 45for angles 3 and 5.
13. the triangle includes 2 exterior angles so...360 divided by 8 = 45 (this is the measure of each exterior angle of the polygon)
45 x 2 cause as I said it includes 2 exterior angles to get 90. it's a triangle so 180 (the sum of angles in triangle) minus 90 to get 90. so 1 and 2 are both 45 and 3 is 90

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2 years ago

The surface area of the prism below is 264 square units . Find the missing dimensions of this prism. ( picture is in the picture

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Answer:

The missing dimension is 4 units.

Step-by-step explanation:

In the given prism,

Of all the surfaces,

There are three rectangular surfaces and two triangular surfaces

<h2>Analyzing areas of rectangular surfaces:</h2>

1)The two rectangles with dimensions of 15 units and 5 units:

The area of each rectangle = Length of rectangle $\times$ Breadth of rectangle

From the diagram,

Length of rectangle = 15 units,

Breadth of rectangle = 5 units.

Area of each rectangle = 15 $\times$ 5 ;

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Sum of areas of the two rectangles = 2 $\times$ 75

Sum of areas of the two rectangles = 150 square units (equation 1)

2) The rectangle with the dimensions 15 units and 6 units:

The area of thus rectangle= Length of rectangle $\times$ Breadth of rectangle

From the diagram,

Length of rectangle = 15 units,

Breadth of rectangle = 6 units.

Area of the rectangle = 15 $\times$ 6 ;

Area of the rectangle = 90 square units. (equation 2)

From equation 1 and equation 2,

Therefore sum of areas of all rectangles in the prism = 150 + 90

Sum of areas of rectangles = 240 square units.

We also know,

Total surface area of the prism = Sum of areas of triangles + Sum areas of rectangles

Given, Total surface area of prism = 264 square units.

Therefore from the formula,

Sum of areas of triangles = Total surface area - sum of areas of reactangles

Sum of areas of triangles = 264 - 240

Sum of areas of triangles = 24 square units. (equation 3)

Let the missing dimension be 'h units'

<h2>Calculating sum of areas of triangles:</h2>

From diagram,both triangles are congruent,hence have the same area

Area of a triangle = $\frac{1}{2}\times base\times height$

From diagram,

Base = 6 units,

Height = h units.

Area of a triangle = $\frac{1}{2}\times 6\times h$ = 3h square units.

Sum of the areas of both triangles = 3h+3h = 6h square units.

Using equation 3, we get

6h = 24;

h = $\frac{24}{6}$

Therefore,

h = 4 units.

Therefore,

The missing dimension is 4 units.

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