Question

Helpppp!!

Find the area of the polygon.

Answer 1

• 27.5 units²

Explanation:

We know that:

• Area of shape = Area of triangle + Area of parallelogram
• Base₁ of parallelogram = 5 units
• Altitude₁ of parallelogram = 3 units
• Area of parallelogram = Base x Altitude
• Base₂ of triangle = 5 units
• Altitude₂ of triangle = 5 units
• Area of triangle = 1/2 x Base x Altitude.

Work:

• Area of parallelogram = Base₁ x Altitude₁
• => Area of parallelogram = 5 x 3
• => Area of parallelogram = 15 units²
• => Area of triangle = 1/2 x Base₂ x Altitude₂
• => Area of triangle = 1/2 x 5 x 5
• => Area of triangle = 1/2 x 25
• => Area of triangle = 12.5 units²
• => Area of shape = Area of triangle + Area of parallelogram
• => Area of shape = 12.5 + 15
• => Area of shape = 27.5 units²

Hence, the area of the shape is 27.5 units².

Answer 2

27.5 square units

Explanation:

1. Draw segment IL

We can find the area by combining the area of two different shapes.

Polygon area = triangle area + parallelogram area

Now you have a triangle with a height of 5 and a parallelogram with a height of 3.

The triangle and parallelogram both have a base of 5.

2. Triangle area (
`(bh)/(2)`) is
`(5*5)/(2)`=
`(25)/(2) =` 12.5

3. Parallelogram area (multiply just like a triangle bh) = 5*3=15

Add up the two areas, 12.5 + 15 = 27.5

27.5 square units is the answer. (The fourth option from up to down.)

Hope this helps :)

Have a great day!