A smaller triangle is cut out of a larger triangle. The larger triangle is a right triangle with side lengths of 5 millimeters a
nd 12 millimeters. The smaller triangle has side lengths of 4 millimeters and 3 millimeters. What is the area of the shaded region?
1 answer:
Options :
21 mm2
24 mm2
42 mm2
48 mm2
Answer: 24mm^2
Step-by-step explanation:
Given the following :
Side length of larger triangle:
Base = 5mm
Height = 12mm
Side length of smaller triangle :
Base = 4mm
Height = 3mm
Area of triangle :
0.5 × base × height
Area of larger triangle :
0.5 × 12mm × 5mm = 30mm^2
Area of smaller triangle :
0.5 × 4mm × 3mm = 6mm^2
Area of shaded region :
(Area of larger triangle - Area of smaller triangle)
(30mm^2 - 6mm^2) = 24mm^2
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The given shapes area is found to be 4 square yards.
Step-by-step explanation:
Step 1; To determine the area of an indefinite shape we must divide it into the shapes that we know. The shape that is given can be split into a triangle with a rectangle in it.
Step 2; Any given triangles area is half the multiplication of its base value and its height value. In the given diagram, the base of the triangle measures a length of 5 yards and the length from base to top is 4 yards
Area of the triangle = * base * height =
* 5 * 4 = 10 square yards.
The given rectangle measures a length of 3 yards and a width of 2 yards. The area of any given rectangle is the multiplication of its length and width.
Area of the rectangle = Length * Width = 3 yards * 2 yards = 6 square yards.
Step 3; To find the total area of the shape we must subtract the the rectangle's area from the triangle's area.
Area of given shape = Area of the triangle - Area of the rectangle.
Area of given shape = 10 square yards - 6 square yards = 4 square yards.