Question

Determine the area of this composite figure below

Answer 1

The area is 510 in^2.

Explanation:

You need to find two areas. The area of the rectangle and then the area of the triangle above.

The formula for a rectangle's area is base x height. The base is 20 inches, and the height is 15 inches as shown on the side. So, you multiply 20 x 15, and the product is 300.

The formula for a triangle's height is 1/2(base x height). The 3 ft on the side is equal to 36 inches. To find the height of the triangle alone, you take the 36 inches and subtract by 15 inches, resulting in a difference of 21 inches. The base of the triangle is 20 inches, so multiply 20 x 21 = 420. Then multiply 420 by 1/2 (or divide by 2) and you get 210.

Now that we have the areas of both shapes, 210 + 300 = 510.

Answer 2

The area of the composite figure is 510in².

Explanation:

1. Identify the different shapes that form this composite figure.

Check attached image 1.

2. Identify the dimensions of each shape.

a) For the rectangle, we have that the base is 20 inches, and that the height is 15 inches.

b) For the triangle, we see that the base is also 20 inches long, and the height must be the difference between the height of the rectangle and the total height of the composite figure.

3. Convert all the units to a single unit.

First, convert the 3 feet to inches, because we need to have the same unit in order to make the calculations.

We know that 12 inches is 1 feet, therefore, to covert 3 feet to inches we do the following operation:

`3feet*(12inches)/(1feet)`

The feet unit cancel out and the 3 is multiplied by 12, leaving us with the following result:

`36inches`

4. Find the height of the triangle.

Check attached image 2.

So the height of the triangle must given by the following expression:

`36in-15in=21in`

5. Find the individual area of each shape.

a) For the rectangle:

`A=b*h`; where "b" is the length of the base and "h" is the height.

`A=(20in)(15in)=300in^(2).`

b) For the triangle:

`A=(b*h)/(2) =((20in)(21in))/(2) =210in^(2) .`

6. Find the total area.

So if the figured is formed by a triangle and a rectangle, the sum of the area of the 2 shaped equals the area of the composite figure. Let's add up the areas and calculate:

`300in^(2) +210in^(2) =510in^(2) .`

7. Conclude.

The area of the composite figure is 510in².