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2 years ago

What is the area of the trapezoid?

Mathematics

1 answer:

Natali [406]2 years ago

8 0

A trapezoid is a quadrilateral with one pair of parallel sides. The formula for the area of a trapezoid is ↓

Area = $\frac{1}{2}$ (base 1 + base 2) h

The bases of the trapezoid are the parallel sides.

In the trapezoid shown, the bases are 22.2 cm and 8.52 cm and the height of the trapezoid is 9.86 cm. Now, we can plug these numbers into our formula.

$\frac{1}{2}$ (22.2 cm + 8.52 cm) (9.86 cm)

Next, the order of operations tells us that we need to simplify inside the parentheses first. 22.2 + 8.52 = 30.72 cm

$\frac{1}{2}$ (30.72 cm) (9.86 cm)

$\frac{1}{2}$ × 30.72 = 15.36

(15.36 cm) (9.86 cm) = 151.4496 cm²

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Quincy's retirement party will cost $30 if he invites 10 guests. If there are 16 guests, how much will Quincy's retirement party

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Answer:

$48

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2 years ago

Read 2 more answers

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

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2 years ago

Which number is equivalent to 2^−5⋅ 3 ⋅ 2^2 ⋅ 3^3? A. 648 B. 216 C. 81/8 D. 27/8

sesenic [268]

$2^{-5} \cdot 3 \cdot 2^2 \cdot 3^3\\\\=2^{-5 +2} \cdot 3^{1+3}\\\\=2^{-3} \cdot 3^4\\\\=\dfrac{3^4}{2^3}\\\\=\dfrac{81}{8}\\\\\\\text{So, the answer is C.}$