The formula of the surface area of a right triangular prism is (Length × Perimeter) + (2 × Base Area) = (s1 s 1 + s2 s 2 + h)L + bh where “b” is the bottom edge of the base triangle, “h” is the height of the base triangle, “L” is the length of the prism and s1 s 1 , s2 s 2 are the two edges of the base triangle.

The volume of the prism is the area of the base times the height. So to calculate height, divide the volume of a prism by its base area. For this example, the volume of the prism is 500 and its base area is 50.

Prisms are polyhedrons, three-dimensional solids with two identical and parallel polygonal bases or ends. The prism’s height is the distance between its two bases and is an important measurement in the calculation of the prism’s volume and surface area.

Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.

A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Surface Area Formulas:

1. Volume = (1/3)πr2h.
2. Lateral Surface Area = πrs = πr√(r2 + h2)
3. Base Surface Area = πr2
4. Total Surface Area. = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw .

This can be calculated using the Heron’s formula: Base area = 0.25 * √[(a + b + c) * (-a + b + c) * (a – b + c) * (a + b – c)] , where: a, b, c are the sides of a triangular base.

To find the perimeter of a triangle, add up the length of all three sides. . This will give you the height of your prism. So, the height of your prism is 68 centimeters.

(a) The angle between its two lateral faces is called the angle of the prism or the prism angle. When the light ray is allowed to pass through the prism, it makes the emergent ray bend at an angle to the direction of the incident ray. This angle is called the angle of deviation for the prism.

In minimum deviation, the refracted ray in the prism is parallel to its base. In other words, the light ray is symmetrical about the axis of symmetry of the prism. Also, the angles of refractions are equal i.e. r1 = r2. And, the angle of incidence and angle of emergence equal each other (i = e).

The formula for the volume of a rectangular prism is given as: Volume of a rectangular prism = (length x width x height) cubic units. Let’s try the formula by working out a few example problems. The length, width, and height of a rectangular prism are 15 cm, 10 cm, and 5 cm, respectively.

You find the dimensions of the total prism and then divide it by how much each cube’s volume. Next, you find the volume of the cube and divide the total with this volume. Finally, after you have divided, you get the number of individual cubes that fit inside the cube.

Finding Volume of Prisms Using Unit Cubes The cubes represent the volume of the prism. This prism is five cubes by two cubes by one cube. In other words, it is five cubes long, by two cubes high by one cube wide. You can multiply each of these values together to get the volume of the rectangular prism.

Answer: First prism has the greatest volume.

What is volume? Volume is the amount of 3-dimensional space an object occupies. Volume is measured in cubic units. For example, the rectangular prism below has a volume of 18 cubic units because it is made up of 18 unit cubes.

To find the volume of this right rectangular prism, fill it with ¼ inch cubes. It takes 64 – ¼ inch cubes to fill one unit cube. The right rectangular prism can be filled with ¼ inch cubes. It takes 9 x 2 x 4 cubes to fill this right rectangular prism.

Each cube has a volume of 23=8 cm3. 2 3 = 8 cm 3 . Then there can be: 320÷8=40 cubes in the box. 320 ÷ 8 = 40 cubes in the box.

24 cubes

the answer is 40 cubes.

therefore, the volume of cube is, = 0.125 cubic inches.

Total of cubes= 6^4=1296.

1 foot is 12 inches. A cube of 2″ x 2″ = 2″x2″x2″ = 8 cubic inches. A 1 by 1 by 1 foot cube can be cut to 216 cubes of 2″x2″x2″.

What is the maximum number of 2-inch by 2-inch by 2-inch cubes that can be placed in a box that measures 7-inches by 8-inches by 9-inches? I thought the answer would be 5048=63, but that is the maximum.

Triangular prism formulas

1. volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle and length is prism length.
2. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.

The height of a triangle is the distance from the base to the highest point, and in a right triangle that will be found by the side adjoining the base at a right angle.

1 Expert Answer Or area times height. To find the height, divide the volume by the product of base and width. To find the base, divide the area by the width.

Key Points

1. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , is used to find the length of any side of a right triangle.
2. In a right triangle, one of the angles has a value of 90 degrees.
3. The longest side of a right triangle is called the hypotenuse, and it is the side that is opposite the 90 degree angle.

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.

Theorems for proving that triangles are similar

• Similar triangles. Similar triangles are the same shape but not the same size.
• Side Side Side (SSS) If a pair of triangles have three proportional corresponding sides, then we can prove that the triangles are similar.
• Side Angle Side (SAS)

These three theorems, known as Angle – Angle (AA), Side – Angle – Side (SAS), and Side – Side – Side (SSS), are foolproof methods for determining similarity in triangles.

If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.