The base of a triangular prism is a right triangle whose legs are 7cm and 24 cm. The height of the prism is 30cm. What is lateral area of prism?
Triangle b1base
To find the lateral area of a prism, you need to calculate the sum of areas of all the lateral faces. For a triangular prism, there are three lateral faces, which are all rectangles.
To calculate the area of a rectangle, you need to multiply its length by its width. In this case, the length of each rectangle is the height of the prism (30 cm), and the width of each rectangle is the perimeter of the base triangle.
To find the perimeter of the base triangle, you need to add the lengths of all three sides. In this case, the base is a right triangle with legs of 7 cm and 24 cm, so you can use the Pythagorean theorem to find the length of the hypotenuse (which is the third side of the triangle).
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, you can use it to find the hypotenuse:
hypotenuse^2 = 7^2 + 24^2
hypotenuse^2 = 49 + 576
hypotenuse^2 = 625
hypotenuse = √625
hypotenuse = 25 cm
Now that you know the length of the hypotenuse, you can calculate the perimeter of the base triangle:
perimeter = 7 + 24 + 25
perimeter = 56 cm
Finally, you can calculate the lateral area of the prism by multiplying the height by the perimeter:
lateral area = height * perimeter
lateral area = 30 cm * 56 cm
lateral area = 1680 cm^2
So, the lateral area of the prism is 1680 square centimeters.