Question

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Find The area of a trapezoid. If the answer is not an integer leave it in simplest radical form. The figure is not to scale.

A=____ft^2 (type in exact answer using radicals as needed)

Answer 1

42ft^2

Start by splitting the "trapezoid" into two shapes ; triangle and square.

The triangle is a right triangle, so we can use the Pythagorean theorem to find its bottom side so we can find the unknown length of the square. This will also tell us the base of the triangle.

3^2 + b^2 = 5^2

b = 4

This means the square has the dimensions of 9ft by 4ft.

Multiply 9(4) for the area of the square --> A = b(h) = 9(4) = 36ft^2

Now for the triangle,

A= 1/2(b)(h)

base is 4, height is 3 thus:

A=1/2(4)(3) --> 12(1/2) = 6ft^2

Add the area of the triangle and square for the total area:

36ft^2 + 6ft^2 = 42ft^2

Answer 2

To solve such a complex shape, its best we split it into simpler shapes:

⇒ let's cut along the dashed line to form

⇒ a square and a triangle

Area of the triangle

⇒
`(1)/(2) *base*height`

⇒ however we don't know the base (dashed line)

(using Pythagorean theorem) ⇒
`dashed-line=√(5^2-3^2 )=√(25-9)=4`

⇒ now that we know the height, let's solve

`Area-of-triangle = (1)/(2)*4*3=2*3=6ft^2` <-- area of triangle

Area of the rectangle

⇒
`length * width`

• length (longer side of rectangle) --> 9ft
• width (shorter side of rectange) --> dashed line --> 4ft

⇒ so:

`Area-of-rectangle= 9*4=36ft^2` <-- area of rectangle)

Combined Area = Area of triangle + Area of rectangle = 6 + 36 = 42ft^2

Answer: 42

Hope that helps!