the base of a given triangular prism is a right angled triangle with AB=5cm,AC=12cm and the height of the prism =20cm. Angle A=90 degrees so calculate the surface area of the prism
In a right angled triangle where angle A is a right angle the Hypotenuse BC square equals AB square plus AC square
5 square plus 12 square equals 169 cm square square root 169 = 13
Therefore, BC= 13
To find the surface area of the prism
you have to find the area of the equal triangles and the area of the other three rectangular faces
area of the triangle is 5 X 12 = 60 divided by 2 = 30
the other triangle is equal
Now you go to the three rectangles
they have same height 20 which is the the same length for all
Now the width of the rectangles are the same length of the sides of the right angled triangle which are 5, 12 and 13
Therefore the area of the rectangle is length X width
Knowing the length is 20 X 5 = 100
20X12 = 240
20X13= 260
Add the area of the same triangles 30 each = 60
Now add and find the total
To find the surface area of the prism, we need to calculate the area of each face and then sum them together.
1. Base Triangle:
The base triangle is a right-angled triangle with AB = 5 cm and AC = 12 cm. Using the formula for the area of a triangle, we can find the area of the base triangle.
Area of triangle = (base * height) / 2
= (AB * AC) / 2
= (5 cm * 12 cm) / 2
= 30 cm²
Therefore, the area of the base triangle is 30 cm².
2. Lateral Faces:
The triangular prism has three lateral faces, which are rectangles. The length of each lateral face is equal to the perimeter of the base triangle, and the width is equal to the height of the prism.
Perimeter of triangle = AB + AC + BC
We need to find the length of BC. Since angle A is 90 degrees, triangle ABC is a right-angled triangle. We can use the Pythagorean theorem to find the length of BC.
BC² = AB² + AC²
BC² = 5 cm² + 12 cm²
BC² = 25 cm² + 144 cm²
BC² = 169 cm²
BC = √169 cm
BC = 13 cm
Perimeter of triangle = AB + AC + BC
= 5 cm + 12 cm + 13 cm
= 30 cm
Now we can calculate the area of each lateral face.
Area of each lateral face = length * width
= 30 cm * 20 cm
= 600 cm²
Since there are three lateral faces, the total area of the lateral faces is 3 * 600 cm² = 1800 cm².
3. Total Surface Area:
The total surface area of the prism is the sum of the area of the base triangle and the lateral faces.
Total surface area = area of base triangle + area of lateral faces
= 30 cm² + 1800 cm²
= 1830 cm²
Therefore, the surface area of the given prism is 1830 cm².
To calculate the surface area of the triangular prism, we need to find the areas of each face and then add them up.
1. The area of the base:
Since the base of the triangular prism is a right-angled triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base (AB) is given as 5 cm, and the height (AC) is given as 12 cm.
Area of the base = (1/2) * 5 cm * 12 cm = 30 cm²
2. The area of the other two rectangular faces:
The triangular prism has two rectangular faces, each with a length equal to the base (AB) and a width equal to the height of the prism.
Area of each rectangular face = length * width = 5 cm * 20 cm = 100 cm²
3. The area of the two triangular faces:
To find the area of a triangle, we need to know the lengths of two sides and the included angle.
In this case, we have a right-angled triangle, so we can find the area using the formula:
Area = (1/2) * base * height
The two triangular faces have the same dimensions as the base triangle, so the areas will be the same.
Area of each triangular face = (1/2) * 5 cm * 12 cm = 30 cm²
4. Calculate the total surface area:
To get the total surface area, we add up the area of each face.
Total surface area = 2 * area of rectangular face + 2 * area of triangular face + area of base
= (2 * 100 cm²) + (2 * 30 cm²) + 30 cm²
= 200 cm² + 60 cm² + 30 cm²
= 290 cm²
Therefore, the surface area of the given triangular prism is 290 cm².