1. A = 64 cm²
2. A = 240 yd²
3. A = 220.5 cm²
4. A = 193.4 m²
Step-by-step explanation:
1. We want to split this figure into two rectangles. We know the top figure is a rectangle because a rectangle has four right angles. For the bottom rectangle, because the sides are all perpendicular, all of the angles are also right angles.
Because they're rectangles, opposite sides are congruent. So now you can find the measures of the sides.
Refer to the image below for the rest.
Don't forget to add up the two areas for the total area of the whole figure.
2. We want to split this figure into a triangle and a rectangle.
Because the bottom figure has four right angles, we know that it's a rectangle. Therefore, its side measures are 24, 24, 8, and 8 because opposite sides of a rectangle are congruent.
For the triangle, because the sum of the triangle's base and two other segments is 24, we can use 24 - (6 + 6) = base. So the triangle base is 12.
Do this same thing to find the height of the triangle.
Refer to the image below for the rest.
Don't forget to add up the two areas for the total area of the whole figure.
3. We want to split this figure into a triangle and semicircle.
We're already given that the height is 15 and part of the base is 8, but there is no way to assume that the other part of the base is also 8. Remember, it's not to scale.
We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent, so the two radii present are both 8.
Because of Reflexive Property, the other part of the triangle base is now proven to also be 8.
Refer to the image below for the rest.
Don't forget to add up the two areas for the total area of the whole figure.
4. We want to split this figure into a rectangle and semicircle.
For the rectangle, because the sides are all perpendicular, all of the angles are also right angles. So we can prove that it is a rectangle.
Because this is a rectangle, opposite sides are congruent. So we have the sides of 15, 7, 15, and 7.
We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent.
Because of Reflexive Property, we know that the diameter of the circle is 15. The radius is half the diameter, meaning all radii are 1/2 (15), or 7.5.
Refer to the image below for the rest.
Don't forget to add up the two areas for the total area of the whole figure.
