Answer:
<em>Answer: B. 38 mm</em>
Step-by-step explanation:
<u>The Perimeter of a Shape</u>
The perimeter of a given shape is the sum of all exterior lengths surrounding the shape.
The figure shows a shape where all the external measures are given except the leftmost side.
This length is the sum of 3 mm + 10 mm = 13 mm.
Now calculate the perimeter:
P = 4 mm + 3 mm + 10 mm + 8 mm + 13 mm = 38 mm
Answer: B. 38 mm
I'm assuming you want the total surface area.
This is a trapezoidal prism. The bases are the parallel faces running horizontal (parallel to the ground) and they are congruent trapezoids. The lateral sides are rectangles.
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Lateral Faces:
The back face (hidden from view) is a rectangle that is 12 inches by 3 inches, so it has an area of 12*3 = 36 sq inches
The front slant faces on the left and right are each 3*5 = 15 sq inches in area
The front center lateral face has area of 6*3 = 18 sq inches
The total lateral surface area is 15+18+15+36 = 84 sq inches
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The bases are each the same trapezoid. The trapezoid has two parallel sides of 12 and 6 inches. Call this b1 and b2. The height of the trapezoid is h = 4. Imagine the trapezoid is laid flat in a 2D perspective instead of a 3D one.
The area of one trapezoid is...
A = h*(b1+b2)/2
A = 4*(12+6)/2
A = 4*(18)/2
A = 72/2
A = 36
So the area of both base faces combined is 2*36 = 72
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The total surface area is then found by adding the total lateral surface area (84) and the total base area (72) to get 84+72 = 156
Final Answer: 156 square inches
Answer:
Isosceles triangle.
Step-by-step explanation:
In order to determine the nature of the triangle, we will need to get the sides XY, XZ and YZ using the distance formula;
For XY;
X(-4,2), Y(4.2)
XY = √(2-2)²(4-(-4)²)
XY = √(4+4)²
XY = √8²
XY = 8
For XZ;
X(-4,2), Z(0, - 1)
XZ = √(-1-2)²(0-(-4))²
XZ = √(-3)²+4²
XZ = √9+16
XZ = √25
XZ = 5
For XZ;
Y(4.2), Z(0, - 1)
YZ = √(-1-2)²(0-(4))²
YZ = √(-3)²+(-4)²
YZ = √9+16
YZ = √25
YZ = 5
Since XZ = YZ = 5, this shows that two sides are equal. Hence the triangle is an isosceles triangle.
NB: Isosceles triangle only have two of its sides and angles equal
Answer:
x = 24
Step-by-step explanation:
The angle bisector creates proportional corresponding line segments on either side of it. That is ...
(35 mm)/(56 mm) = (x +4) mm/(44.8 mm)
Multiplying by 44.8, you have
44.8 · (35/56) = x + 4
28 = x + 4 simplify
24 = x subtract 4
