SOLUTION: V-QRST is a rectangular pyramid with an edge VS, base QRST. QR = 3/8 m, RS = 5/8 M, and VS = 2/3 m. How many square centimeters are there on its lateral surface? Round off the answ

Algebra ->  Polygons -> SOLUTION: V-QRST is a rectangular pyramid with an edge VS, base QRST. QR = 3/8 m, RS = 5/8 M, and VS = 2/3 m. How many square centimeters are there on its lateral surface? Round off the answ      Log On


   

Question 1198364: V-QRST is a rectangular pyramid with an edge VS, base QRST. QR = 3/8 m, RS = 5/8 M, and VS = 2/3 m. How many square centimeters are there on its lateral surface? Round off the answer to the nearest integer.
Answer by onyulee(41) About Me  (Show Source):
You can put this solution on YOUR website!
**1. Understand the Problem**
* We have a rectangular pyramid.
* We know the base dimensions (QR = 3/8 m, RS = 5/8 m) and the slant height (VS = 2/3 m).
* We need to find the lateral surface area in square centimeters.
**2. Convert Units**
* Convert the given dimensions from meters to centimeters:
* QR = (3/8) * 100 = 37.5 cm
* RS = (5/8) * 100 = 62.5 cm
* VS = (2/3) * 100 = 66.67 cm (approximately)
**3. Calculate Slant Heights**
* The rectangular pyramid has four triangular faces. We need to find the slant height of each triangle.
* **For the two triangles with base QR:**
* Slant height (l1) = √(VS^2 - (RS/2)^2)
* l1 = √(66.67^2 - (62.5/2)^2)
* l1 ≈ 56.69 cm
* **For the two triangles with base RS:**
* Slant height (l2) = √(VS^2 - (QR/2)^2)
* l2 = √(66.67^2 - (37.5/2)^2)
* l2 ≈ 64.04 cm
**4. Calculate the Area of Each Triangle**
* **For the two triangles with base QR:**
* Area = (1/2) * base * height = (1/2) * QR * l1
* Area = (1/2) * 37.5 * 56.69
* Area ≈ 1062.81 cm²
* **For the two triangles with base RS:**
* Area = (1/2) * base * height = (1/2) * RS * l2
* Area = (1/2) * 62.5 * 64.04
* Area ≈ 2001.25 cm²
**5. Calculate the Total Lateral Surface Area**
* Lateral Surface Area = 2 * (Area of triangle with base QR) + 2 * (Area of triangle with base RS)
* Lateral Surface Area = 2 * 1062.81 + 2 * 2001.25
* Lateral Surface Area ≈ 6128.12 cm²
**6. Round Off the Answer**
* Rounding to the nearest integer: 6128.12 ≈ 6128
**Therefore, the lateral surface area of the rectangular pyramid is approximately 6128 square centimeters.**