Surface Area - combined straight edge objects 04:27 minutes

Video Transcript

Transcript Surface Area - combined straight edge objects

Home alone at last! Mom, Dad, Buster, and the rest of the MacCaulay family are all gone for the day, so Calvin is happy to have the house all to himself. But something about this van that's been parked across the street all morning is making Calvin skittish. Suddenly, he remembers a story he heard on the news about a kid who saved his family’s valuables from a couple of inept robbers. Although the robbers didn't get the family's stuff, they did get away. Calvin decides that he's not taking any chances: it's time to burglarproof the house! Luckily, Calvin has some supplies to foil the robbers' dastardly plan: Super-slick soap? Check. Industrial strength fly paper? Check. Luckily, Calvin is a master at calculating the area of faces of 3 dimensional shapes, so he doesn’t waste his supplies. The news said that the burglars like to enter through the chimney, just like Santa Claus, so the first trap Calvin wants to set is to completely cover the roof in fly paper. Look! The roof is in the shape of a square pyramid. It’s called a square pyramid because it has a square base. This one measures 45 feet by 45 feet, and the triangle faces each have a height of 25.5 feet, and meet at a point called the apex. We can plug these measurements into the formula for the area of a triangle to find the surface area of the roof. The area of a triangle equals one half times the base times the height. Plugging in the numbers for the base and the height, forty-five times 25.5 is 1,147.5. Dividing this by two gives us 573.75, and multiplying the result by 4 for the number of triangle faces, we get 2,295 square feet for the surface area of the roof. That's a lot of fly paper! Just in case the burglars decide to come through the front door, Calvin wants to cover the front steps in some super-slippery soap. The stairs are a composite shape composed of rectangular prisms. Remember, a prism is made up of faces that include two identical bases and flat sides. First, we divide the prisms into faces. Then, we add all the relevant areas together. Making up the faces of the rectangular prisms are 12 rectangles labeled 'A', each measuring 12 inches by 8 inches. The area of each rectangle is found by multiplying the length times the width. Then, we multiply the area of one rectangle by the total number of rectangles, 12. That gives us a total area of 1,152 square inches. For the sides of the prisms, there are 3 sides labeled 'B' with dimensions of 40 inches by 8 inches, and 3 tops labeled 'C', with dimensions 40 inches by 12 inches. All of these faces are rectangles, so we can calculate the surface area of each face by multiplying the length times the width. For the faces labeled B, we have 3 rectangles, each with the dimensions 40 inches times 8 inches which gives us 960 square inches. For the faces labeled C, we have 3 rectangles, each with the dimensions 40 inches times 12 inches, giving us 1,440 square inches. Now, just add the areas of the relevant faces together to get the total visible surface area. Calvin needs enough soap to cover 3,552 square inches. Getting back to Calvin, It looks like the booby traps have been set and Calvin is feeling pretty safe and secure. It must be the burglars! They’re going to find out they picked the wrong kid to mess with! Oops. Sorry! It looks like that was just the delivery guy's van parked across the street.