Equations for Geometric Problems Practice
1. An illustration shows a triangle with three vertical cylinders at its base placed at equal distance. The base of the triangle is 22 feet and distance from the vertex to the base of the triangle is represented by a dotted line which is 6 feet. The triangle in the picture shows the top of the entrance to a classical building. How would you write an equation to find the area of this triangle?
___ ft.²
2. An illustration shows a purse made with a trapezium at the bottom and half loop at the top. The base of the trapezium is 25 centimeters, the upper side is 15 centimeters and the distance between parallel sides is 13 centimeters. The picture shows the front panel of a handbag. Substitute the values shown into the formula for the area of a trapezoid to create an equation that can be used to find the area of the front of the handbag. What is the equation?
___ cm²
3. An illustration shows a rectangular prism with a length of 6 inches, a width of 4 inches, and a height of 3 inches. The picture shows the dimensions of a brick. Substitute the values shown into the formula for the volume of a rectangular prism to create an equation that can be used to find the volume of the brick. What is the equation?
___ in.³
4. An illustration shows a triangle. The base measures 13 centimeters The vertical height is indicated by a dashed perpendicular line from the top vertex to the base and measures 14 centimeters. Write and solve an equation to find the area of the triangle. What is its area?
___ cm²
5. An illustration shows a rectangular prism. The length measures 6 inches, the width measures 2 inches, and the height measures 11 inches. Write and solve an equation to find the volume of the box. What is its volume?
___ in.³
1. Area of triangle = (1/2) * base * height
Area = (1/2) * 22 * 6 = 66 ft²
2. Area of trapezoid = (1/2) * (base1 + base2) * height
Area = (1/2) * (25 + 15) * 13 = 260 cm²
3. Volume of rectangular prism = length * width * height
Volume = 6 * 4 * 3 = 72 in.³
4. Area of triangle = (1/2) * base * height
Area = (1/2) * 13 * 14 = 91 cm²
5. Volume of rectangular prism = length * width * height
Volume = 6 * 2 * 11 = 132 in.³