Question 1198364
**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.**