Question

Find the area. Round to the nearest hundredth when necessary. Be sure you are showing all work to find each figure.

Answer 1

`\displaystyle 62\:in.^2`

Step-by-step Step-by-step explanation:

▽
`\displaystyle (hb)/(2) = A, (1)/(2)bh = A, or\:(1)/(2)hb = A`

▯
`\displaystyle hb = A`

All edges meet at right angles, therefore resulting in this:

`\displaystyle 62 = 56 + 6 \Rightarrow 62 = 7 * 8 + 4 * 1(1)/(2)`

I am joyous to assist you at any time.

Answer 2

Additional requirements in figure :-

Mark point :-

• A
• B
• C
• D
• E

Draw a straight line from E to AB .

And the point line joins mark it as "F" .

It will generate quadrilateral FBCD.

we get to know In quadrilateral left angle is 90°

How ?

{

proof :

As three angles are given 90° So third angle will also be 90°

Reason:

→ Sum of interior angles = 2 (no. of angles - 2 × 180°

→Sum of interior angles = (4-2 × 180°)

→Sum of interior angles = (2 × 180°)

→Sum of interior angles = 360°

}

✿Now let the left angle be x

• 90° +90° + 90° + x = 360°
• 180° + 90° + x = 360°
• 270° + x = 360
• x = 360° - 270°
• x = 90°

we know :

Area of rectangle = Length × Breadth

STEPS :

• Area of rectangle = Length × Breadth

• Area of rectangle = 7 × 8

• Area of rectangle = 56 in²

Now let's find EF :

• EF = BD - EC

• EF = 7 - 4

• EF = 3 in

To find A

F :

• A•F = AB - CD

• A•F = 12 - 8

• A•F = 4 in

In triangle AFE:

• EF is base of triangle
• A•F is height of triangle

We know :

Area of triangle =( Height × Base)/2

Steps :

• Area of triangle = (Height × Base)/2
• Area of triangle = (4 × 3)/2
• Area of triangle = 12/2
• Area of triangle = 6 in²

To find area of figure :

• Area of figure = Area of rectangle + Area of triangle
• Area of figure = 56 + 6
• Area of figure = 62 in²

______________________

~WindyMint