Step-by-step explanation:
Given that,
We have to find the value of m∠E.
Here, two sides are equal, thus it is an isosceles triangle. As the two sides are equal, so their angles must be equal. So, ∠E and ∠D will be equal. Let us assume the measures of both ∠E and ∠D as x.
→ Sum of all the interior angles of ∆ = 180°
→ ∠E + ∠D + ∠F = 180°
→ 116° + x + x = 180°
→ 2x = 180° – 116°
→ 2x = 64°
→ x = 64° ÷ 2
→<u> x = 32°</u>
Henceforth,
→ m∠E = x
→ m∠E = 32°
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Answer:
Step-by-step explanation:
In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...
A = 1/2bh
where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.
You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.
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For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).
In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.
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The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...
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By way of example, we can "show work" for problem 1:
1. S = Ph +2B
S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2
Answer:
The length on the blueprint for an actual length of 65 feet is
Step-by-step explanation:
Given:
Scale of the blueprint is
Length of one side of the house is 65 feet.
Now, as per given data;
1 foot in actual = on the blueprint.
Therefore, using unitary method, we can find find the length on the blueprint for an actual length of 65 feet by multiplying 65 and . Therefore,
Length on the blueprint for 65 feet is given as:
Therefore, the length on the blueprint for an actual length of 65 feet is
Answer:
The dimensions of the pool are:
Width: 8.944 feet
Length: 17.888 feet
Step-by-step explanation:
From Geometry, the area of a rectangle (), measured in square feet, is determined by the following equations:
(1)
Where:
- Width, measured in feet.
- Length, measured in feet.
If we know that ,
and
, then we get the following second order polynomial:
(1)
And we solve the expression for :
Then, the dimensions of the pool are, respectively:
and