An image of a rocket is shown. The rocket is made up of a triangle, a rectangle, and a trapezoid. The triangle at the top of the rocket has a base of length 3 inches and a height of 4 inches. The rectangle in the middle of the rocket has a height of 10 inches and a length of 3 inches. The trapezoid at the bottom of the rocket has one base of length 3 inches at the top, another base of length 5 inches at the bottom, and a height of 2 inches.
Use familiar figures to find the area of the figure shown. Show all work.
Since we know the shapes that make up the rocket, we can find their individual areas and add them together to find the total area of the rocket.
Area of triangle: (1/2) base x height = (1/2) x 3 inches x 4 inches = 6 square inches
Area of rectangle: length x width = 3 inches x 10 inches = 30 square inches
Area of trapezoid: (1/2) (base 1 + base 2) x height = (1/2) (3 inches + 5 inches) x 2 inches = 8 square inches
Total area of rocket = 6 square inches + 30 square inches + 8 square inches = 44 square inches
Therefore, the area of the figure shown (the rocket) is 44 square inches.
To find the area of the rocket, we need to find the area of each individual shape and then add them together.
First, let's find the area of the triangle. The formula for the area of a triangle is:
Area = 0.5 * base * height
For the triangle at the top of the rocket, the base is 3 inches and the height is 4 inches. So the area of the triangle is:
Area = 0.5 * 3 inches * 4 inches = 6 square inches
Next, let's find the area of the rectangle. The formula for the area of a rectangle is:
Area = length * height
For the rectangle in the middle of the rocket, the length is 3 inches and the height is 10 inches. So the area of the rectangle is:
Area = 3 inches * 10 inches = 30 square inches
Finally, let's find the area of the trapezoid. The formula for the area of a trapezoid is:
Area = 0.5 * (base1 + base2) * height
For the trapezoid at the bottom of the rocket, base1 is 3 inches, base2 is 5 inches, and the height is 2 inches. So the area of the trapezoid is:
Area = 0.5 * (3 inches + 5 inches) * 2 inches = 4 inches * 2 inches = 8 square inches
Now, we can add up the areas of all the shapes to find the total area of the rocket:
Total Area = Area of triangle + Area of rectangle + Area of trapezoid
= 6 square inches + 30 square inches + 8 square inches
= 44 square inches
Therefore, the area of the figure shown, which represents the rocket, is 44 square inches.