A rectangle has an area of 465 cm².
A triangle has a height of 32 cm and a base width of 24 cm.
Which shape has the larger area?
To determine which shape has a larger area, we can compare the areas of the rectangle and the triangle.
First, let's calculate the area of the rectangle. We know that the area of a rectangle is given by the formula:
Area = length × width
Since the area of the rectangle is 465 cm², we can set up the equation:
465 = length × width
Next, let's calculate the area of the triangle. The formula for the area of a triangle is given by:
Area = 1/2 × base × height
For the triangle in question, the base width is 24 cm, and the height is 32 cm. Substituting these values into the formula, we have:
Area = 1/2 × 24 × 32
Now, we can simplify the expression:
Area = 12 × 32
Area = 384 cm²
Comparing the two areas, we find that the area of the rectangle is 465 cm², while the area of the triangle is 384 cm².
Since 465 is greater than 384, the rectangle has a larger area than the triangle.
To determine which shape has the larger area, we will compare the areas of the rectangle and the triangle.
1. Area of the Rectangle:
The formula to calculate the area of a rectangle is given by:
Area = length × width
In this case, the area of the rectangle is given as 465 cm². However, since we are not provided with the length or width of the rectangle, we need further information to determine the dimension of the rectangle.
2. Area of the Triangle:
The formula to calculate the area of a triangle is given by:
Area = (base × height) / 2
Given that the height of the triangle is 32 cm and the base width is 24 cm, we can calculate its area as follows:
Area = (24 cm × 32 cm) / 2
Area = 768 cm²
Based on the calculations, the triangle has a larger area (768 cm²) compared to the unknown area of the rectangle (465 cm²). Therefore, the triangle has the larger area.
Area of triangle = (1/2)(base)(height)
= (1/2)(24)(32) = ....
compare it to 465 cm^2