Question

Основание прямой теугольной пирамиды служит прямоугольный треугольник с катетами 3см и 4 см.Высота 10см Найти площадь полной поверхности

Answer 1

Основанием пирамиды служит прямоугольный треугольник,следовательно найдем его площадь:

1.По теореме Пифагора находим гипотенузу:

а=√в²+с²=√16+9=√25=5 см.

2.Найдем площадь прямоугольного треугольника-основания пирамиды:

по двум катетам

S осн = а*в/2 = 12/2 = 6 см²

3.Найдём площадь боковой стороны:

S бок = 1/2*Р осн*l .

где Р осн-периметр основания пирамиды

l - апофема пирамиды

S бок = 1/2*12*10 = 60 см

4.Найдём полную площадь пирамиды:

S полн =S бок+ 2*Sосн = 60+2*6=72 см²

Answer 2

Given Information:

We are given that the base of a right triangular pyramid is a right triangle with legs measuring 3 cm and 4 cm. The height of the pyramid is 10 cm. We need to find the total surface area of the pyramid.

Solution:

To find the total surface area of the pyramid, we need to calculate the areas of the triangular faces and the base.

1. Area of the triangular faces: - The triangular faces of the pyramid are congruent right triangles. - The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height. - In this case, the base and height of each triangular face are given as 3 cm and 4 cm, respectively. - Therefore, the area of each triangular face is: (1/2) * 3 cm * 4 cm = 6 cm².

2. Area of the base: - The base of the pyramid is a right triangle with legs measuring 3 cm and 4 cm. - The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height. - In this case, the base and height of the base triangle are given as 3 cm and 4 cm, respectively. - Therefore, the area of the base triangle is: (1/2) * 3 cm * 4 cm = 6 cm².

3. Total surface area: - The total surface area of the pyramid is the sum of the areas of the triangular faces and the base. - Since there are four triangular faces, the total surface area is: 4 * 6 cm² = 24 cm².

Therefore, the total surface area of the given pyramid is 24 cm².