Question

pre-algebra ic sem 2 fall 2025
surface area of composite
figures
what is the surface area of the composite solid?
1,808 m²
1,658 m²
1,958 m²
1,508 m²

Explanation:

Step1: Calculate the area of the triangular parts

The area of a triangle is \(A=\frac{1}{2}bh\). Here \(b = 8m\) and \(h=6m\). The area of one triangle is \(\frac{1}{2}\times8\times6=24m^{2}\). There are \(2\) such triangles, so \(2\times24 = 48m^{2}\).

Step2: Calculate the area of the slanted rectangles

The area of a rectangle is \(A = lw\). The slanted rectangles have \(l = 8m\) and \(w = 10m\). There are \(2\) such rectangles, so \(2\times8\times10=160m^{2}\).

Step3: Calculate the area of the large rectangles of the prism

The large rectangles of the prism have two types:

• One type with \(l = 25m\) and \(w = 15m\), area \(A_1=25\times15 = 375m^{2}\), and there are \(2\) of them, so \(2\times375=750m^{2}\).
• Another type with \(l = 25m\) and \(w = 10m\), area \(A_2=25\times10=250m^{2}\), and there are \(2\) of them, so \(2\times250 = 500m^{2}\).

Step4: Calculate the area of the bottom rectangle of the prism

The bottom rectangle of the prism has \(l = 15m\) and \(w = 10m\), area \(A_3=15\times10=150m^{2}\).

Step5: Calculate the total surface area

Sum up all the areas: \(48 + 160+750+500+150=1608 + 200=1808m^{2}\)

Answer:

\(1,808m^{2}\)