Question

100 POINTS 100 POINTS 100 POINTS 100 POINTS IF YOU ANSWER THIS PROBLEM

Answer 1

Answer:

Option A

The Area of the given figure is 5x²/2 + 3x/2 - 4

Step-by-step explanation:

For a given Trapezoid

side a = x + 7

side b = 4x + 1

height (h) = x - 1

Now, Area of Trapezoid

Formula:

A = ½ (a + b) × h

A = ½ (x + 7 + 4x + 1) × (x - 1)

A = ½ (5x + 8) × (x - 1)

A = ½ (5x² - 5x + 8x - 8)

A = ½ (5x² + 3x - 8)

A = 5x²/2 + 3x/2 - 8/2

A = 5x²/2 + 3x/2 - 4

Thus, The Area of the given figure is

5x²/2 + 3x/2 - 4

-TheUnknownScientist

Answer 2

$\boxed{\large{\bold{\blue{ANSWER~:) }}}}$

In this given trapizoid,

we have to find the area.

we know that,

Area of a trapizoid =$\sf{\dfrac{1}{2}(a+b)×h }$

where,

• a=side
• b=base
• h=height

But,

In the given trapizoid

• a=x+7
• b=4x+1
• h=x-1

According to the question,

• $\sf{Area_{(trapizoid)}=\dfrac{1}{2}(x+7+4x+1)×(x-1) }$

• $\sf{Area_{(trapizoid)}=\dfrac{1}{2}(5x+8)×(x-1) }$

• $\sf{Area_{(trapizoid)}=\dfrac{1}{2}[(5x(x-1)+8(x-1)] }$

• $\sf{Area_{(trapizoid)}=\dfrac{1}{2}[(5x^2-5x)+(8x-8)] }$

• $\sf{Area_{(trapizoid)}=\dfrac{1}{2}(5x^2-5x+8x-8) }$

• $\sf{Area_{(trapizoid)}=\dfrac{1}{2}(5x^2+3x-8) }$

• $\sf{Area_{(trapizoid)}=\dfrac{5x^2}{2}+\dfrac{3x}{2}-\dfrac{8}{2} }$

• $\bold{Area_{(trapizoid)}=\dfrac{5x^2}{2}+\dfrac{3x}{2}-4 }$

Therefore,

• Area of the trapizoid=$\sf{\frac{5x^2}{2}+\frac{3x}{2}-4 }$

• Option A is correct.