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meriva
3 years ago
11

In the picture below, ABCD is a rectangle. If the area of triangle ABE is 40, what is the area of the triangle?

Mathematics
1 answer:
MariettaO [177]3 years ago
7 0

Area of the rectangle: 112

Step-by-step explanation:

Picture is missing: find it in attachment.

The area of a triangle is given by

A=\frac{1}{2}bh

where

b is the length of the base

h is the height

For triangle ABE, we know that

A = 40 (area)

h = 8 (height)

So we can find the length of the base AE:

AE=b=\frac{2A}{h}=\frac{2(40)}{8}=10

Now we observe that the base of the rectangle, AD, is the sum of AE and DE, therefore:

AD=AE+DE=10+4=14

We also know the height of the rectangle AB is 8, and that the area of a rectangle is

A=bh

where b is the base and h the height. Therefore, the area of this rectangle is

A=bh=(AD)(AB)=(14)(8)=112

Learn more about area of figures:

brainly.com/question/4599754

brainly.com/question/3456442

brainly.com/question/6564657

#LearnwithBrainly

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#2 is the one I need help with
sleet_krkn [62]

Step-by-step explanation:

By arc sum Postulate of a circle:

2 x + 3x + 4x = 360°

9x = 360°

x = 360°/9

x = 40°

3x = 3* 40° = 120°

By inscribed angle theorem:

m\angle 1= \frac {1}{2} \times 3x\\\\\therefore m\angle 1= \frac {1}{2} \times 120°\\\\\huge \red {\boxed {\therefore m\angle 1= 60°}}

By tangent secant theorem:

m\angle 2 = \frac {1}{2} \times 3x\\\\\therefore m\angle 2 = \frac {1}{2} \times 120°\\\\\huge \purple {\boxed {\therefore m\angle 2 = 60°}}

Since, measure of central angle is equal to the measure of its corresponding minor arc.

m\angle 3 = 3x\\\\\huge \pink {\boxed {\therefore m\angle 3 = 120°}}

By angle sum Postulate of a triangle:

m\angle 3 + 2 m\angle 4 = 180°\\\\120° + 2 m\angle 4 = 180° \\\\2 m\angle 4 = 180°- 120° \\\\2 m\angle 4 = 60° \\\\m\angle 4 = \frac {60°}{2} \\\\\huge \orange {\boxed {m\angle 4 =30°}}

3 0
3 years ago
Rico and his friend eat some lasagna. Rico eats 1/9 of lasagna, and his friend eats 1/18 of the lasagna. How much of the lasagna
Blizzard [7]

Answer:

\frac{5}{6} of the lasagna is left

<u>Step-by-step explanation:</u>

Given:

Amount of lasagna Rico eats = 1/9

Amount of lasagna His friend eats = 1/18

To Find:

The amount  lasagna is left =?

Solution:

Total lasagna ate by both Rico and his friend = Amount of lasagna Rico eats +  Amount of lasagna His friend eats

Total lasagna ate by both Rico and his friend = \frac{1}{9} + \frac{1}{18}

Total lasagna ate by both Rico and his friend = \frac{2}{19} + \frac{1}{18}

Total lasagna ate by both Rico and his friend = \frac{3}{18}

Total lasagna ate by both Rico and his friend = \frac{1}{6}

The amount  lasagna is left = 1 - Total lasagna ate by both Rico and his friend.

The amount  lasagna is left = 1 - \frac{1}{6}

The amount  lasagna is left =\frac{6-1}{6}

The amount  lasagna is left =\frac{5}{6}

4 0
3 years ago
Name the place value of highlighted digit 35.052
DanielleElmas [232]
The highlighted 5 in 35.052 is in the hundredths place. 
3 0
3 years ago
Read 2 more answers
3
Alexus [3.1K]

Answer:

1. 10mn - 35      2. 8rs -2r + 16

Step-by-step explanation:

10mn - 35

8rs -2r + 16

3 0
2 years ago
A mix for 5 servings of instant potatoes requires 1 1/4 cups of water. The amount of water needed to make 11 servings is?
Vladimir [108]
2.75 cups or 2 3/4 cup
6 0
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