The area of a figure can be found by decomposing

it into smaller, non-overlapping figures.

The area of the large figure is equal to the

sum of the areas of the smaller figures.

Start by decomposing the trapezoid into 2 congruent triangles and a rectangle.

Next, find the area of one of the triangles and the rectangle.

Area of Rectangle | = | length × width |

| = | 13 cm × 12 cm |

| = | 156 sq cm |

Area of Triangle | = | $\frac{1}{2}$× base × height |

| = | $\frac{1}{2}$× 5 cm × 12 cm |

| = | 30 sq cm |

Then, find the sum of the 3 areas.

156 sq cm + 30 sq cm + 30 sq cm = 216 sq cm

So, the area of the trapezoid is 216 square centimeters.

The net shows that the prism has two triangular faces with a base of 9 inches and a height of 8 inches and three rectangular faces with dimensions of 9 inches by 12 inches.

First, find the area of one of the triangular faces.

Area of Triangle | = | $\frac{1}{2}$× base × height |

| = | $\frac{1}{2}$× 9 in. × 8 in. |

| = | 36 sq in. |

Next, find the area of one of the rectangular faces.

Area of Rectangle | = | length × width |

| = | 12 in. × 9 in. |

| = | 108 sq in. |

Then, add the areas of the faces.

Remember there are two triangular faces and three rectangular faces.

2 × 36 sq in. + 3 × 108 sq in. = 396 sq in.

So, the surface area of the triangular prism is 396 square inches.